Turito Academy

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In <img src="data:image/png;base64,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" class="Wirisformula" alt="capital delta A B C comma sum left parenthesis left parenthesis b squared minus c squared right parenthesis right parenthesis divided by a c o s invisible function application A equals" width="219" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«mi»A«/mi»«mi»B«/mi»«mi»C«/mi»«mo»,«/mo»«mo»§#8721;«/mo»«mo»(«/mo»«mo»(«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mi»a«/mi»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#8289;«/mo»«mi»A«/mi»«mo»=«/mo»«/math»'/>

Solution for the question - in /_\abc,sum((b^(2)-c^(2)))//acosa= 2delta '/> a '/>0s

In /_\abc,sum((b^(2)-c^(2)))//acosa= -Turito

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Solution for the question - 4(x rarr pi//6)((3sin x-sqrt3cos x)//(6x-pi))= (-1)//sqrt3 '/> -sqrt3 '/> 1//sqrt3 '/> sqrt3 '/>

4(x rarr pi//6)((3sin x-sqrt3cos x)//(6x-pi))= -Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis left parenthesis c o s invisible function application 4 x plus a c o s invisible function application 2 x plus b right parenthesis divided by x to the power of 4 right parenthesis" width="267" height="18" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»(«/mo»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«mo»)«/mo»«mo»(«/mo»«mo»(«/mo»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#8289;«/mo»«mn»4«/mn»«mi»x«/mi»«mo»+«/mo»«mi»a«/mi»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#8289;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»)«/mo»«mo»/«/mo»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»)«/mo»«/math»'/> is finite then the values of a,b are respectively

Solution for the question - if [(x rarr0)((cos 4x+acos 2x+b)//x^(4)):} is finite then the values ofa,b are respectively 4,5-4,3 '/> -5,-4 '/> 5,-4 '/>

If [(x rarr0)((cos 4x+acos 2x+b)//x^(4)):} is finite then t-Turito

In this question we are <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals tan to the power of negative 1 end exponent open parentheses x close parentheses" width="111" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»tan«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«/math»'/> and we have to find the value of <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 1 of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction" width="123" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»1«/mn»«/mrow»«/munder»«mfrac»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»'/> Step1: Putting the value of limit By putting the value of limit we are getting both numerator and denominator as zero. That is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=" class="Wirisformula" alt="0 over 0" width="18" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»0«/mn»«mn»0«/mn»«/mfrac»«/math»'/> form. Step2: Using L'Hôpital's rule By differentiating both numerator and denominator we get <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 1 of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator 1 end fraction" width="83" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»1«/mn»«/mrow»«/munder»«mfrac»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mn»1«/mn»«/mfrac»«/math»'/> =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 1 right parenthesis" width="32" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/> We have to find the value of <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 1 right parenthesis" width="32" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/> Step3: Finding the value of <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 1 right parenthesis" width="32" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/>. <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAATCAYAAACeJVPaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAjlJREFUeNpjYBgF1AZqQFwLxBdGg2LogcVAnAbE/webw7KAuINEPR1QfSMN/B+ocGQCYnE0MT0gPk6mR45C9Y9GHo3D0QOI30HxFSBmQdJoQKalxkB8eIhHBC5MauTRLBxBEfUUyXAtKG0AtZQScBhqOTXBuyGW82gajkFAvByLeBcQ51BoaR4Z5Twl9cpgjDyahmM9EJdjEd8BxLZYxJNxGNQMlUMGlkC8l4ZFGTrwA+KTQPwLiG8BsTWOwA0F4rtA/AOIDwKxLA0jj2bhuA4tMCKR5D4BMRsOR55Da9wkAvEULOrYoOaQWqfgq1vw5bylSMV+IrT+RtcbCs0N8kjqDtKgfqRLON7AkfL+EGjg9EHZLgRy168BKjaZsNgN0utIhDpqApqFI8jh38iwFAR2A7E9dFRBeBBGHja1/6lgJjUjj6JwNAfi/TgU48vuIFAANRBfH4TexWYttK77g8OMgYg8moUjqI6bjydFWOOQA4mvgWb5SDyWUrvBgi+gZ0LrM45BlvNoFo6TGCBjcgwkNHGVgHgTEHMBMQ8Qn8GT3XOg5lAT/IIW99hS+GAsNmkWjqDWphcODdg6l6JAvA3NEh8GyMAsvTrpF3Ck0htITWxpaJP7OZQ9kJFHs3B8h1bMoIPjSGUxGzSypbGoWw5tOdFjeAzUWnyJJcD1oE3vX9C+Hqg+b4SqHcjIo0k4ikJTJj4wOjBNHUDVcJwALWaIGbrKIGOIqwtPXTpSAdXCEZQVg0bDc+gBACx51Jz+XundAAAAyHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1zdXA+PG1pPnRhbjwvbWk+PG1yb3c+PG1vPi08L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtZmVuY2VkPjxtaT54PC9taT48L21mZW5jZWQ+PC9tYXRoPuDYP8UAAAAASUVORK5CYII=" class="Wirisformula" alt="f left parenthesis x right parenthesis equals tan to the power of negative 1 end exponent open parentheses x close parentheses" width="111" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»tan«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«/math»'/> =&gt; <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAAAjCAYAAAAjZxB6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAA1pJREFUeNrtnDFoFEEUhpcgIYjYSJAgIgQRsZCAhYiICBYiwSIQxDIIIiGInVUQsQkpRMTGSkTEJliIBCGIHEFCQEIKCxEsRWxSWEg4Aud73judrLN7M3uzszO7/wc/5O5m9i7vvZt5M29ukwQAv1wnLWievy+vAVAbNkgHlcczpMcwC6gbl0gP5O+LpHcwCagrK6TzpE3SAZgjfo6R5sWh4B+3SW3SSZiiHjwn3SB1YIq/nCUtSfpyLYYPPJuxgs5jQfo1jQ7s+Idx0mvSXtI+0scqU5eh1KqYnfQ11YannLWC1//QwCkrK9CbZMdR0nIqsCdl1qtkRbwl+kTaI056pjHyRMH3OEVajTxos2Qb6E2x4zDpFemQ5rWXEnfe4KD+phj+hOKkq0q7CXHQIKyKo1yyFdmIHqoda8+UfLt0ThpTHi+S5gZ8r1sF8tJB8uAQA923HbEgFu6S7mieT+fnb0nnNO1syrtnEreFgn4pxBXSetLd0voiK39dEEzL/7tNapEOlxjovu2IQJf8SQ0UddvndKrtT8m5dJiWd4flOrY5cF4unOfIF0oqNiPrj3TfaRlljyjtWiXk877siEDP4LPhCLbTZzFrWt5tV5S6DGnem/teMGjnEt92RKCLU385cBBjWt6tKtB1bTsVBEfZdiw6M5r2jUH/wenJe0MH5U25jEl513fqMi+5+U7GNaoI9LLtiBFdA+fkTw3brmgWcz1My7uuF6N5jnwi+fdIYCO6bzsi0IlHSfdMhglZ22I25d05uY5L2pKC6UbOEFMX33ZEoMuuy2XDtrpCh215t4xCx2bG6MeL7N62HFfmeJvue7K7SldFoPu2IwI96VYVRyzarym5o215t6zSNe+a/NA4lD/nhoz467IeuSdtqwz0UO0YC721VlsGjKP9OozKCGcDDnW5AXYcHE5XZ2Uwy+ShTO1FyvE3C/RbtFgLNAXY0Q3beS/y9DcFG4HI4XpDC2YALgj1Z4FjksaNw0XABSH+LJC/fG+S3adrAXBCx1Mfk5Gct2L3wyUgxkA3PabMQX4c7gAxj+gmx5RtDqkBEGSg425eIIpAH+SIcA/czQs0YjGKu3mB2gd6dHfzAgh02z5B3c0LINDL6BPU3bxAcwO8zO280u7m9RtH1HCwi5CJTAAAATd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPic8L21vPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bXN1cD48bWk+dGFuPC9taT48bXJvdz48bW8+LTwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdXA+PG1mZW5jZWQ+PG1pPng8L21pPjwvbWZlbmNlZD48bW8+KzwvbW8+PG1mcmFjPjxtaT54PC9taT48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjwvbWF0aD5bx3xvAAAAAElFTkSuQmCC" class="Wirisformula" alt="f apostrophe left parenthesis x right parenthesis equals tan to the power of negative 1 end exponent open parentheses x close parentheses plus fraction numerator x over denominator 1 plus x squared end fraction" width="186" height="35" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»tan«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«mo»+«/mo»«mfrac»«mi»x«/mi»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/math»'/> by putting the value of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAANCAYAAADFVhxbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJpJREFUeNpjYBhYoAbEtUB8gWGQgcVAnAbE/xkGKcDrsGQg7sAi3gyVGzCHgcA5IBZH4icC8RQCBhLCVHGYBxD3QdkuQLx3MEQlDOwGYntoThEeTA4rAOJfQKxHpIF0iUprIF4Djc7IwZIrlYB4ExBzATEPEJ8ZDFEpCsTb0BziAy0AB8xhbEC8Doilscgth+ZUWjqInDQ5cAAAg6UzdRinE6IAAABddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPng8L21pPjxtbz49PC9tbz48bW4+MTwvbW4+PC9tYXRoPuPh974AAAAASUVORK5CYII=" class="Wirisformula" alt="x equals 1" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mn»1«/mn»«/math»'/>, <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 1 right parenthesis space equals space pi over 4 plus 1 half" width="113" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math»'/> =&gt;<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator pi plus 2 over denominator 4 end fraction" width="48" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»§#960;«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mn»4«/mn»«/mfrac»«/math»'/>

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals x t a n left parenthesis negative 1 right parenthesis invisible function application x" width="130" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»x«/mi»«mi»t«/mi»«mi»a«/mi»«mi»n«/mi»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#8289;«/mo»«mi»x«/mi»«/math»'/> then <img src="data:image/png;base64,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" class="Wirisformula" alt="l i m subscript left parenthesis x rightwards arrow 1 right parenthesis   left parenthesis f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis right parenthesis divided by left parenthesis x minus 1 right parenthesis equals" width="235" height="20" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»l«/mi»«mi»i«/mi»«msub»«mi»m«/mi»«mo»(«/mo»«/msub»«mi»x«/mi»«mo»§#8594;«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#8202;«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»=«/mo»«/math»'/>

Solution for the question - if f(x)=x tan(-1)x then {:lim_(()x rarr1)(f(x)-f(1))//(x-1)= (pi+3)//4 '/> (pi+2)//4 '/> (pi+1)//4 '/> pi//4 '/>

If f(x)=x tan(-1)x then {:lim_(()x rarr1)(f(x)-f(1))//(x--Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f colon R rightwards arrow R" width="56" height="16" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»:«/mo»«mi»R«/mi»«mo»§#8594;«/mo»«mi»R«/mi»«/math»'/> be a positive increasing function with <img src="data:image/png;base64,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" class="Wirisformula" alt="L t left parenthesis x rightwards arrow infinity right parenthesis space space left parenthesis f left parenthesis 3 x right parenthesis right parenthesis divided by left parenthesis f left parenthesis x right parenthesis right parenthesis equals 1 space" width="212" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»(«/mo»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mn»3«/mn»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«/math»'/>then <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA8JJREFUeNrtWl+EVFEYv9YaybxkrHlYiaxkH7L0sFbSSzKSZMhaPSWystJD9JDVQ5axDytrRNZK1lrWSpIsSbLGGCVZSXrpae3bSrKyhuk72zdcx/m+e757zpnZrvn4Me6ce8/9/e453797o8iv3QJUouxYBTl1So+Q+pm4SPmNAGpd5OqDg8hOAepR9qyG3Hzq0QcodkE/ExcJvwXAtS5zTcVhF28kzWQjGVzUpwEbHvUoAXYQXwD9xPgzgDXAL8Ae4DOxoFy52PIbAPwg1oYr16AchgCbzAWHiPDDhaUs2AYK5xqm1UPdij3QYWb8e8AEIB8bW8NjvrnY8LsPmA7ENSiHK4AV5mJlwLLh+CxgKsOL+rYw/6P0KBP62up3LMHppOWSxK8PvfRAB7l64/AAcI+4kPqvFUN83DrgrOGcG8RED/E/qU1jtLC1q4CPGMJV+J4BFLTcbglD4xvkaLIxwFvBvJQelL7UeJP9cdTZxCWJn4oOi4G5BuOwit6aMup/tWhyxDmftELhOqCacoeu4Fw2IXgcc9ISYhk34zbgBN7HphayxnDh65bDeW3NpMdzzSlMWOqnP7iao84mLkn8uPTEJ9cgHL4DBhly3zAE6tZkzlELag5/nxd6PN2K6HlbWIkfYsYuMdFG5XpfAUcMY+4aqvUIizVbazL6HRXq1zbFtYEFpKvOewJ+STmwT67eOai86XdCXrUrJNY2FdrPYQpQSBjbEmCVuc5j4ngVz20Qm+Iy4EKARe2in9p8L4j7SqOzZFEvJHRdml1aK1YcRgHvmIuMYkVuG4LidgcnTNPvpTz1k4Q55xkPvoXXWDcs7IqhIPKRfnD6cvodxwVtU0vY6CwJ3VwbLwRX7xxU3vM0oVh4xuwuKiy2+61zHtpRkpy6jBVxfEOsYcGTxzyxhR6h7Z1nCA8vLRRNenD6UvqdRE952GJOW50lRRbVxgvBNQiHeUzMKXvEtGKoNo3yMi/xoeTRyxYcFrW0+zGO+WADxdSL3EmMPj/RI1EPcAo5urT0lL43BeOLmF71W8wn0dnExXSMa+P55hqKw37FWmJuvsq0dUzFhBLjtXZjl4gC7qCbj5cvSt+LgvGv0FMnmVRn2xcXXBvPN9dQHPZfZVIFmcpXhmO5qCknqsfyoBwSGyRSiNJ/tKDTviava3nhTkK3Rh/PFchRSp0lr5glG9mFa0gOztb7oInWQ3mi7QOgn+sHTQeBaygOpE1G2fr0dJbJDW31+BD969lWuqyfiYsrv05zDc2hZ4L0pdzj2jn7C4qdcepMcefaAAABPXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5MPC9taT48bWk+dDwvbWk+PG1vPig8L21vPjxtaT54PC9taT48bW8+JiN4MjE5Mjs8L21vPjxtbz4mI3gyMjFFOzwvbW8+PG1vPik8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4oPC9tbz48bWk+ZjwvbWk+PG1vPig8L21vPjxtbj4yPC9tbj48bWk+eDwvbWk+PG1vPik8L21vPjxtbz4pPC9tbz48bW8+LzwvbW8+PG1vPig8L21vPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+KTwvbW8+PC9tYXRoPoVhE20AAAAASUVORK5CYII=" class="Wirisformula" alt="L t left parenthesis x rightwards arrow infinity right parenthesis space space left parenthesis f left parenthesis 2 x right parenthesis right parenthesis divided by left parenthesis f left parenthesis x right parenthesis right parenthesis" width="181" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»(«/mo»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mn»2«/mn»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«/math»'/>

Solution for the question - if f:r rarr r be a positive increasing function with (t(x rarroo)(f(3x))//(f(x))=1 then f(x rarr oo)(f(2x))//f(x)) 33//2 '/> 2//3 '/>

If f:r rarr r be a positive increasing function with (t(x-Turito

Solution for the question - 4(pi rarr oo)[1//n^(2)sec^(2)1//n^(2)+2//n^(2)sec^(2)4//n^(2)+cdots++1//nsec 1]= 1//2tan 1 '/> tan 1 '/> 1//2cos ec1 '/> 1//2 secl '/>

4(pi rarr oo)[1//n^(2)sec^(2)1//n^(2)+2//n^(2)sec^(2)4//n^(2)+c-Turito

Solution for the question - 4(n rarroo)(1+2^(4)+3^(4)+cdots+n^(4))//n^(5)-4(1+2^(3)+3^(3)+..+n^(3))//n^(4)= 1//4 '/>zero1//30 '/> 1//5 '/>

4(n rarr oo)(1+2^(4)+3^(4)+cdots+n^(4))//n^(5)-4(1+2^(3)+3^(3)+-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis plus x comma y space" width="172" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»y«/mi»«mo»)«/mo»«mo»+«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»§#160;«/mo»«/math»'/>and <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis 5 right parenthesis equals 2 comma f to the power of apostrophe left parenthesis 0 right parenthesis equals 3" width="118" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mn»5«/mn»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mn»0«/mn»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«/math»'/> then <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of apostrophe left parenthesis 5 right parenthesis" width="32" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mn»5«/mn»«mo»)«/mo»«/math»'/> is

Solution for the question - if f(x+y)=f(x)f(y)+x,y and f(5)=2,f^(')(0)=3 then f^(')(5) is 2610

If f(x+y)=f(x)f(y)+x,y and f(5)=2,f^(')(0)=3 then f^(')-Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="L t ┬ left parenthesis n rightwards arrow infinity right parenthesis left parenthesis 1 to the power of p plus 2 to the power of p plus 3 to the power of p plus midline horizontal ellipsis. plus n to the power of p right parenthesis divided by n to the power of left parenthesis p plus 1 right parenthesis" width="332" height="23" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»§#9516;«/mo»«mo»(«/mo»«mi»n«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«mo»)«/mo»«mo»(«/mo»«msup»«mn»1«/mn»«mi»p«/mi»«/msup»«mo»+«/mo»«msup»«mn»2«/mn»«mi»p«/mi»«/msup»«mo»+«/mo»«msup»«mn»3«/mn»«mi»p«/mi»«/msup»«mo»+«/mo»«mo»§#8943;«/mo»«mo».«/mo»«mo»+«/mo»«msup»«mi»n«/mi»«mi»p«/mi»«/msup»«mo»)«/mo»«mo»/«/mo»«msup»«mi»n«/mi»«mo»(«/mo»«/msup»«mi»p«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/> is

Solution for the question - {:4t(pi rarr oo)(1^(rho)+2^(rho)+3^(rho)+cdots.+n^(rho))//pi^(()rho+1) is 1//(beta+2) '/> 1//rho-1//(rho-1) '/> 1//(1-rho) '/> 1//(beta+1) '/>

{:4t(pi rarr oo)(1^(rho)+2^(rho)+3^(rho)+cdots.+n^(rho))//pi^((-Turito

For <img src="data:image/png;base64,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" class="Wirisformula" alt="x element of R L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis right parenthesis to the power of x equals" width="255" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8712;«/mo»«mi»R«/mi»«mi»L«/mi»«mi»t«/mi»«mo»(«/mo»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«mo»)«/mo»«mo»(«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»)«/mo»«msup»«mo»)«/mo»«mi»x«/mi»«/msup»«mo»=«/mo»«/math»'/>

Solution for the question - for x in r(t(x rarr oo)((x-3)//(x+2))^(x)=:} e5e-5e-1 '/>e

For x in r(t(x rarr oo)((x-3)//(x+2))^(x)=:} -Turito

In this question we are given <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 2 right parenthesis equals 6" width="59" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«mo»=«/mo»«mn»6«/mn»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAARCAYAAABjEtTjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAWlJREFUeNpjYKAMZAFxBwnqO6B6BhVgAmJxJP5/IL6LpkYPiI+TYfZRqN5BATyA+B0UXwFiFqhnF2JxtAEW/WpAXAvEF3CYbwzEh+ngDx+ou3ECkMeeInlCCylmw5HUGUA9iw0sBuI0AhYdhnqaVoAHiK8R8mwQEC/HIg7SJInE7wLiHAIW4rMoj8S8TiqYCcTJhDxbD8TlWMTR8+sOILalwLOWQLyXRh61RjIbpxvWQSVhOBJJzhxN7ScgZqPAs2xQM3DpI4TxmXsJiOWJcAPDDSCWJSL0/hCh5j8B+V80iNUOtOz1H191841IQwejZ/WwFJo43QBKqvuJNHgwJuOTQKxCrBtAeXQ+kZ7dDS0IBlMBRVIATYLWj8QASqueHKgZtAZ4S2MvIg3B16ggxrO0blQQdAOoechBgkHHcbRxCSUhejUXcXpWFIifk1H6DbmOwARo/UpO8y2DRH1dJJQLNAHG0DbxsAcAJDh3bP2omU4AAACFdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmY8L21pPjxtbz4nPC9tbz48bW8+KDwvbW8+PG1uPjE8L21uPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1uPjQ8L21uPjwvbWF0aD7gpFc5AAAAAElFTkSuQmCC" class="Wirisformula" alt="f apostrophe left parenthesis 1 right parenthesis equals 4" width="59" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»=«/mo»«mn»4«/mn»«/math»'/> and we have to find <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as h minus greater than 0 of fraction numerator f left parenthesis 2 h plus 2 plus h squared right parenthesis minus f left parenthesis 2 right parenthesis over denominator f left parenthesis h minus h squared plus 1 right parenthesis minus f left parenthesis 1 right parenthesis end fraction" width="196" height="45" style="vertical-align:-18px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»h«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/mrow»«/munder»«mfrac»«mrow»«mi»f«/mi»«mo»(«/mo»«mn»2«/mn»«mi»h«/mi»«mo»+«/mo»«mn»2«/mn»«mo»+«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»h«/mi»«mo»-«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/math»'/> Step1: Putting the value of limit By putting the value of limit we are getting both numerator and denominator as zero. That is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=" class="Wirisformula" alt="0 over 0" width="18" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»0«/mn»«mn»0«/mn»«/mfrac»«/math»'/> form. Step2: Using L'Hôpital's rule  By differentiating both numerator and denominator we get, <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as h minus greater than 0 of fraction numerator f apostrophe left parenthesis 2 h plus 2 plus h squared right parenthesis left parenthesis 2 plus 2 h right parenthesis over denominator f apostrophe left parenthesis h minus h squared plus 1 right parenthesis left parenthesis 1 minus 2 h right parenthesis end fraction" width="214" height="45" style="vertical-align:-18px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»h«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/mrow»«/munder»«mfrac»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»2«/mn»«mi»h«/mi»«mo»+«/mo»«mn»2«/mn»«mo»+«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«mo»(«/mo»«mn»2«/mn»«mo»+«/mo»«mn»2«/mn»«mi»h«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»h«/mi»«mo»-«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»1«/mn»«mo»-«/mo»«mn»2«/mn»«mi»h«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/math»'/> By putting the value of limit we get <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as h minus greater than 0 of fraction numerator f apostrophe left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis over denominator f apostrophe left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis end fraction" width="102" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»h«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/mrow»«/munder»«mfrac»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/math»'/> =&gt;<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 2 cross times 6 over denominator 4 end fraction equals 3" width="72" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»2«/mn»«mo»§#215;«/mo»«mn»6«/mn»«/mrow»«mn»4«/mn»«/mfrac»«mo»=«/mo»«mn»3«/mn»«/math»'/> Hence, the value of the limit is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAHxJREFUeNpjYIAARyDeBsTfgPgHEN8C4glALMyABvYDcRAQsyGJGQDxDgYiwSdiFCkB8Q18CsSBOBHqTi9sCv6j4QJCVgoCcQAQnwRie2LcyANVTBT4QYwiPaiHUMBBIA4FYhYgZoLG1H0gjkdXaAvEW6BW/YDGlA8DOQAAUB8ZG37zNZsAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjM8L21uPjwvbWF0aD5kKqj+AAAAAElFTkSuQmCC" class="Wirisformula" alt="3" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«/math»'/>. <h3 class="LC20lb MBeuO DKV0Md"> </h3>

<img src="data:image/png;base64,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" class="Wirisformula" alt="L t left parenthesis h rightwards arrow 0 right parenthesis left parenthesis f left parenthesis 2 h plus 2 plus h squared right parenthesis minus f left parenthesis 2 right parenthesis right parenthesis divided by left parenthesis f left parenthesis h minus h squared plus 1 right parenthesis minus f left parenthesis 1 right parenthesis right parenthesis" width="378" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»(«/mo»«mi»h«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«mo»)«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mn»2«/mn»«mi»h«/mi»«mo»+«/mo»«mn»2«/mn»«mo»+«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»h«/mi»«mo»-«/mo»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»)«/mo»«/math»'/>, given that <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of apostrophe left parenthesis 2 right parenthesis equals 6" width="59" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mn»2«/mn»«mo»)«/mo»«mo»=«/mo»«mn»6«/mn»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="f to the power of apostrophe left parenthesis 1 right parenthesis equals 4" width="59" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»=«/mo»«mn»4«/mn»«/math»'/>

Solution for the question - {:u_(()h rarr0)(f(2h+2+h^(2))-f(2)))//(f(h-h^(2)+1)-f(1)) ,given thatf^(')(2)=6 and f^(f)(1)=4 is equal to (-3)//2 '/> is equal of 3//2 '/>

{:u_(()h rarr0)(f(2h+2+h^(2))-f(2)))//(f(h-h^(2)+1)-f(1)) ,gi-Turito

Solution for the question - lim(x rarr0)(x tan 2x-2x tan x)//((1-cos 2x)^(2))= -1//2 '/> 1//2 '/>-22

Lim(x rarr0)(x tan 2x-2x tan x)//((1-cos 2x)^(2))= -Turito

In this question we are given <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis a right parenthesis equals 2" width="55" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«/math»'/>, <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis a right parenthesis equals space 1" width="63" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="g apostrophe left parenthesis a right parenthesis equals 2" width="62" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»`«/mo»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«/math»'/>. We have to find <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than a of fraction numerator g left parenthesis x right parenthesis f left parenthesis a right parenthesis minus g left parenthesis a right parenthesis f left parenthesis x right parenthesis over denominator x minus a end fraction" width="185" height="41" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mi»a«/mi»«/mrow»«/munder»«mfrac»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»-«/mo»«mi»g«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»a«/mi»«/mrow»«/mfrac»«/math»'/> Step1: Putting the value of the limit By putting the value of the limit in the expression, we get, both numerator and denominator as zero. That is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=" class="Wirisformula" alt="0 over 0" width="18" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»0«/mn»«mn»0«/mn»«/mfrac»«/math»'/> form. Step2: Using L'Hôpital's rule By differentiating both numerator and denominator we get, <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than a of fraction numerator g apostrophe left parenthesis x right parenthesis f left parenthesis a right parenthesis minus g left parenthesis a right parenthesis f apostrophe left parenthesis x right parenthesis over denominator 1 end fraction" width="193" height="41" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mi»a«/mi»«/mrow»«/munder»«mfrac»«mrow»«mi»g«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»-«/mo»«mi»g«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mn»1«/mn»«/mfrac»«/math»'/> By putting the value of limits we get, <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than a of fraction numerator g apostrophe left parenthesis x right parenthesis f left parenthesis a right parenthesis minus g left parenthesis a right parenthesis f apostrophe left parenthesis x right parenthesis over denominator 1 end fraction equals 2 cross times 2 minus left parenthesis negative 1 right parenthesis cross times 1" width="328" height="41" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mi»a«/mi»«/mrow»«/munder»«mfrac»«mrow»«mi»g«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»-«/mo»«mi»g«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mn»1«/mn»«/mfrac»«mo»=«/mo»«mn»2«/mn»«mo»§#215;«/mo»«mn»2«/mn»«mo»-«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#215;«/mo»«mn»1«/mn»«/math»'/> =&gt;<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAF9JREFUeNpjYICA/3gwCsAQwAUGWOEvIP4ExNuAuAiIefBpYAFiYyCuBeIbQKxBjC1uQHyQWCf9IEaRDhDfRRdcB8SWQMwExR5QRUHoCkOB+BYQ/wHid0C8CohNGcgBAFkNGiuTv/xSAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj41PC9tbj48L21hdGg+xM93IwAAAABJRU5ErkJggg==" class="Wirisformula" alt="5" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»'/> Hence, the value of the limit is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAF9JREFUeNpjYICA/3gwCsAQwAUGWOEvIP4ExNuAuAiIefBpYAFiYyCuBeIbQKxBjC1uQHyQWCf9IEaRDhDfRRdcB8SWQMwExR5QRUHoCkOB+BYQ/wHid0C8CohNGcgBAFkNGiuTv/xSAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj41PC9tbj48L21hdGg+xM93IwAAAABJRU5ErkJggg==" class="Wirisformula" alt="5" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«/math»'/>

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis a right parenthesis equals 2 comma f to the power of apostrophe left parenthesis a right parenthesis equals 1 comma g left parenthesis a right parenthesis equals negative 1 comma g to the power of factorial left parenthesis a right parenthesis equals 2 comma" width="270" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«msup»«mi»f«/mi»«mo»`«/mo»«/msup»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mn»1«/mn»«mo»,«/mo»«mi»g«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»,«/mo»«msup»«mi»g«/mi»«mo»!«/mo»«/msup»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«mo»,«/mo»«/math»'/> then the value of  <img src="data:image/png;base64,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" class="Wirisformula" alt="L i m subscript left parenthesis x rightwards arrow a right parenthesis invisible function application left parenthesis g left parenthesis x right parenthesis f left parenthesis a right parenthesis minus g left parenthesis a right parenthesis f left parenthesis x right parenthesis right parenthesis divided by left parenthesis x minus a right parenthesis" width="284" height="20" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»i«/mi»«msub»«mi»m«/mi»«mo»(«/mo»«/msub»«mi»x«/mi»«mo»§#8594;«/mo»«mi»a«/mi»«mo»)«/mo»«mo»§#8289;«/mo»«mo»(«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»-«/mo»«mi»g«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»a«/mi»«mo»)«/mo»«/math»'/> is <span style="font-size: 11.0pt; font-family: 'Cambria Math',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">,

Solution for the question - if f(a)=2,f^(')(a)=1,g(a)=-1,g^(')(a)=2 then the value of{:lim_(()x rarr a)(g(x)f(a)-g(a)f(x))//(x-a) is , none of these5

If f(a)=2,f^(')(a)=1,g(a)=-1,g^(')(a)=2 then the value of-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="G left parenthesis x right parenthesis equals negative √ left parenthesis 25 minus x squared right parenthesis" width="152" height="20" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»G«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mo»§#8730;«/mo»«mo»(«/mo»«mn»25«/mn»«mo»-«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«/math»'/> then <img src="data:image/png;base64,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" class="Wirisformula" alt="L i m subscript left parenthesis x rightwards arrow 1 right parenthesis invisible function application left parenthesis G left parenthesis x right parenthesis minus G left parenthesis 1 right parenthesis right parenthesis divided by left parenthesis x minus 1 right parenthesis" width="233" height="20" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»i«/mi»«msub»«mi»m«/mi»«mo»(«/mo»«/msub»«mi»x«/mi»«mo»§#8594;«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#8289;«/mo»«mo»(«/mo»«mi»G«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»G«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/math»'/> has the value

Solution for the question - if g(x)=-sqrt((25-x^(2))) then {:lim_(()x rarr1)(g(x)-g(1))//(x-1)has the value none of these-sqrt24 '/> 1//5 '/> 1//24 '/>

If g(x)=-sqrt((25-x^(2))) then {:lim_(()x rarr1)(g(x)-g(1-Turito

In this question we are given <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis space equals space square root of fraction numerator x minus sin open parentheses x close parentheses over denominator x plus cos squared open parentheses x close parentheses end fraction end root" width="161" height="47" style="vertical-align:-20px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msqrt»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«msup»«mi»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfrac»«/msqrt»«/math»'/> and we have to find the limit <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAdCAYAAADxTtH0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAohJREFUeNrtWEFEREEYHsmTdFtJkuiQdMiSJEmiQ7KHRNIhSSQrSZcOHZJEOqysRJIOSWR16JBIkpXESock0THdOnRIstQ/+lbTa+a9N/t6b3fzPj67758388w3M///z8/Y/0CUuKTZZwn9ChZFxAqTrZF4keV45+ivhQ+HNi/RTXwGb4jFwoTCWY7ZREwWmhh84o/CpBvwG4YYbpCEKK7E8BN9xF2JfZk44XLsSV1/42RnZJ57iCniGzFBLIO9k3gJO1/NOo3vzxFnJPYjYrvEPqqY4ALaRLQST7wQY4x4KmzjYWIcAon2IQjmBPsYO8NBoe2FaCj6XZmc7QhxVfKegXH+XIwEPL4IvhPWJfa0xvfviNUSe9rG4cbwv8tm9d+9EKNE8V6JCz/ERXxVtNkJekzsIF4TQ36LoeN8nYrRgiMmg9Ux4ZjCRK1yCc+OiRdicB+xZbHybYq2NhzbmMnPML8cqBdixOGYmUZorSUeEEsRzVIWx2QC4xSEGPuIRjLIkq5y4qFp8hHitpdJl19iPCsccAYXgk8wIF6V5L1dRBjX6XiuwFf5yeYd3y9qucAK8gsnqfJ4Flf4ZQtflHdowp0kQIAAAQIUEpJCzC1C4aTGYd8toYhjhWkkP2vsZ92yl7iJ1Ls+H8SIsO/SWkwzrG0Q73HDVGGW2M++KlxxZKBRiDBkEiyUD4Jc49q7oWiPsp9VJzPTTF3OmzQ9z6PPgqR+MZAPYsSR9Rma/bh4D8RmmyxRRAPuHa+ma3gldlBO0YVjcos7gQ6c+Ix+rDg/ArweuYfv7EGQRey8Hfa7ROgreH3xDBOKSrbuX4H7FF4k7pCk3sMQy8ilEAYiSZ3w/OAwOvwrfALZlKsho2BqVQAAAL10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXVuZGVyPjxtaT5saW08L21pPjxtcm93PjxtaT54PC9taT48bW8+JiN4MjE5Mjs8L21vPjxtbz4mI3gyMjFFOzwvbW8+PC9tcm93PjwvbXVuZGVyPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48L21hdGg+tlmkLgAAAABJRU5ErkJggg==" class="Wirisformula" alt="limit as x rightwards arrow infinity of f left parenthesis x right parenthesis" width="67" height="29" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/> Step1: Using Standard limits We know that <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow infinity of fraction numerator sin open parentheses x close parentheses over denominator x end fraction equals 0" width="118" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mfrac»«mrow»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mi»x«/mi»«/mfrac»«mo»=«/mo»«mn»0«/mn»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow infinity of fraction numerator cos squared open parentheses x close parentheses over denominator x end fraction equals 0" width="129" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mfrac»«mrow»«msup»«mi»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mi»x«/mi»«/mfrac»«mo»=«/mo»«mn»0«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow infinity of f left parenthesis x right parenthesis space equals space square root of fraction numerator 1 minus begin display style fraction numerator sin open parentheses x close parentheses over denominator x end fraction end style over denominator 1 plus begin display style fraction numerator cos squared open parentheses x close parentheses over denominator x end fraction end style end fraction end root" width="206" height="94" style="vertical-align:-44px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msqrt»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mi»x«/mi»«/mfrac»«/mstyle»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«msup»«mi»cos«/mi»«mn»2«/mn»«/msup»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«mi»x«/mi»«/mfrac»«/mstyle»«/mrow»«/mfrac»«/msqrt»«/math»'/> =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow infinity of f left parenthesis x right parenthesis space equals space square root of fraction numerator 1 minus begin display style 0 end style over denominator 1 plus begin display style 0 end style end fraction end root" width="153" height="45" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msqrt»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«mstyle displaystyle=¨true¨»«mn»0«/mn»«/mstyle»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«mstyle displaystyle=¨true¨»«mn»0«/mn»«/mstyle»«/mrow»«/mfrac»«/msqrt»«/math»'/> =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow infinity of f left parenthesis x right parenthesis space equals space 1" width="102" height="29" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/>

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals √ left parenthesis left parenthesis x minus sin invisible function application x right parenthesis divided by left parenthesis x plus cos invisible function application x right parenthesis right parenthesis" width="232" height="20" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»§#8730;«/mo»«mo»(«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«/math»'/> then <img src="data:image/png;base64,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" class="Wirisformula" alt="L t f left parenthesis x right parenthesis space" width="47" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«/math»'/>is

Solution for the question - if f(x)=sqrt(((x-sin x))//(x+cos x)) thenuf f(x) is none of these0[theta '/>1

If f(x)=sqrt(((x-sin x))//(x+cos x)) thenuf f(x) is -Turito

In this question we are given <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis 9 right parenthesis equals 9" width="55" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mn»9«/mn»«mo»)«/mo»«mo»=«/mo»«mn»9«/mn»«/math»'/>,<img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 9 right parenthesis equals 4" width="59" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»9«/mn»«mo»)«/mo»«mo»=«/mo»«mn»4«/mn»«/math»'/> and we have to find the limit of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAuCAYAAADnRg0FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABGJJREFUeNrtW09IFkEUHyQ+RCKKEg8WSYREhAgVFRUheAjxEGKUh5AoRESiWx2Cgg6JBxPrEgYdooQwi5AKIkIkwgiTEIlCokN0CAw62IdY9h6+hW3Z+bc7s9+3u/ODH9+3M/tndt/OvDdv58dYPrAWuFIGdLCMk8BX7jFkH8+AZyMc1wPs0zymj45zSBibgD/pl4cKYE2grAH4JuI1X9PxDgmiG/hIUH8UuECcBa7xGasx4jV3Ayct3lMT8ClwEVgEfgIOAjfm2dDom9s5dWjUbz6D7qTfRjJ0HEySwW3dUxuw4CvDNj/Pq5HrgD+AlZx6fFgjIeX9wN6Y1z4Xwb/Hxa+8GvoicFhQfxl4IaQce8bhkPIzHONdpTo/DgBfJniv24Af82ro9+SDwzAWmON2BHpGgXPcdCBwOw28GbJfIaEeVkNtQD/dkoeESBC7gN99wVUYsAdsCSlflgRvA/S/WdJrlyzeczAZcz7LBt4OvEM3eihQdw14XTKlWuTULUuu+wJ4BDgjiXSXNI0VJZu2AXgMOEVtyiQukaFxnvw2UPcFuEdw7D7Gz5aJhm5GvWdJMldOauj2j2pTWR+6MRP11+c79wM/S4btDnpJeD32IKcOy0dp+O4QnD/pYIzRnDrzwGH4Pv2/Abwi2X8I2MWp402vMLJ9AqyiHvROMHT30nmSQgMFZJnHbeBv6sU4d94h2X9MEKWGJUyq2Wo2ym/YVuDdEiRMJoDH6V4x1mgiV9VpMtJTKSsF1gP/AB8ytRz1giCRwugcDT5/iy9Gbch+IyFTONspUJzjj9NQXaRYo9V0SF+uhvZ6kcpUo5qmXrKhMLcfNcr94/leauNmwT6DNH9WSU92M/00Zr/A96fa0Cuc7RYKVooUpXpJjSaaBhTpza833MZ2ST0Oq23MwYihu8hveF+DOinKbQmUn6KXwSGlhh6laDA4x7sVUr7sHmt6DV3J2a/SkN9fcbS7IFHHR7OY5Q4pCcacoZ2hnaGdoR2coR0cTMCEbMchBXCynZwgqmzHIUVQke04ZAAy2U7ScJIbSxDJdkrVnlRKbh5ovo24fHUO+IGtLpmxiTomlu2UE8pecoOGm2Vq34HRsKh8wPVQuBJknNn9fiyT7ejIcGzCmOQGl+F4y18qaJjYarCh2KPvKfTuafb/Mt1aZnf9lUi242+TigzHBoxLbnBxmacsHLDYi2S9G4frKt+2SFGhmxAJQkW2w5ieDMcUrEpuZuiEw4oXj5oVqie/yIs4hykQWcdWFyvE0TDFke34oSrDUX1eJZXcDJEfKJTYX+M+88CvwBP0GxVxZDt+qMhwbMKY5KaZhu45CoJMQ9VHh7kUE/4wimzHg6oMxzZiS25QOjpBb00PRZQ2erHuVMkbKmsNtUNXtuNFu6oyHJuILbkpUFRb79ue5wQvcebRqqOE57vw7X1MPtYUdGU7ujIcU7Auuck6dGQ7ujIck7AuuckDVGU7DimHimzHISNoz9sN/wNv2b0ElCP0eAAAATV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXVuZGVyPjxtaT5saW08L21pPjxtcm93PjxtaT54PC9taT48bW8+LTwvbW8+PG1vPiZndDs8L21vPjxtbj45PC9tbj48L21yb3c+PC9tdW5kZXI+PG1mcmFjPjxtcm93Pjxtc3FydD48bWk+ZjwvbWk+PG1vPig8L21vPjxtaT54PC9taT48bW8+KTwvbW8+PC9tc3FydD48bW8+LTwvbW8+PG1uPjM8L21uPjwvbXJvdz48bXJvdz48bXNxcnQ+PG1pPng8L21pPjwvbXNxcnQ+PG1vPi08L21vPjxtbj4zPC9tbj48L21yb3c+PC9tZnJhYz48L21hdGg+iVUX5gAAAABJRU5ErkJggg==" class="Wirisformula" alt="limit as x minus greater than 9 of fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction" width="122" height="46" style="vertical-align:-19px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»9«/mn»«/mrow»«/munder»«mfrac»«mrow»«msqrt»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/msqrt»«mo»-«/mo»«mn»3«/mn»«/mrow»«mrow»«msqrt»«mi»x«/mi»«/msqrt»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/> Step1: Putting the value of limit By putting the value of limits in the expression, we are getting both numerator and denominator as zero. That is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=" class="Wirisformula" alt="0 over 0" width="18" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»0«/mn»«mn»0«/mn»«/mfrac»«/math»'/> form. Step2: Using L'Hôpital's rule In this rule we differentiate both numerator and denominator. =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 9 of fraction numerator begin display style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator 2 square root of f left parenthesis x right parenthesis end root end fraction end style over denominator begin display style fraction numerator 1 over denominator 2 square root of x end fraction end style end fraction" width="113" height="94" style="vertical-align:-42px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»9«/mn»«/mrow»«/munder»«mfrac»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mn»2«/mn»«msqrt»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/msqrt»«/mrow»«/mfrac»«/mstyle»«mstyle displaystyle=¨true¨»«mfrac»«mn»1«/mn»«mrow»«mn»2«/mn»«msqrt»«mi»x«/mi»«/msqrt»«/mrow»«/mfrac»«/mstyle»«/mfrac»«/math»'/> By putting the value of limit we get, <img src="data:image/png;base64,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" class="Wirisformula" alt="f apostrophe left parenthesis 9 right parenthesis equals 4" width="59" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»`«/mo»«mo»(«/mo»«mn»9«/mn»«mo»)«/mo»«mo»=«/mo»«mn»4«/mn»«/math»'/> Hence, the value of limit is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAE5JREFUeNpjYMAOfID4PwMBwAPE14hROBOIkwkptAbivVA2ToVsQHwJiOUJKewA4hwkPlaFekB8FE0Mq8KTQKxCjML/BDBeQFAB7RSiAADJqxnbA8YC5wAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+NDwvbW4+PC9tYXRoPhlZrqYAAAAASUVORK5CYII=" class="Wirisformula" alt="4" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math»'/>.

If <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis 9 right parenthesis equals 9 comma f to the power of 1 left parenthesis 9 right parenthesis minus 4 comma" width="127" height="18" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mn»9«/mn»«mo»)«/mo»«mo»=«/mo»«mn»9«/mn»«mo»,«/mo»«msup»«mi»f«/mi»«mn»1«/mn»«/msup»«mo»(«/mo»«mn»9«/mn»«mo»)«/mo»«mo»-«/mo»«mn»4«/mn»«mo»,«/mo»«/math»'/> then <img src="data:image/png;base64,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" class="Wirisformula" alt="L t divided by left parenthesis x rightwards arrow t right parenthesis space space left parenthesis √ left parenthesis f left parenthesis x right parenthesis right parenthesis minus 3 right parenthesis divided by left parenthesis √ x minus 3 right parenthesis" width="253" height="20" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mi»t«/mi»«mo»/«/mo»«mo»(«/mo»«mi»x«/mi»«mo»§#8594;«/mo»«mi»t«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8730;«/mo»«mo»(«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«mo»/«/mo»«mo»(«/mo»«mo»§#8730;«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«/math»'/>

Solution for the question - if f(9)=9,f^(1)(9)-4 then 4//(x rarr t)(sqrt((f(x))-3))//(sqrt(x-3)) 3041

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In $capital delta A B C comma sum left parenthesis left parenthesis b squared minus c squared right parenthesis right parenthesis divided by a c o s invisible function application A equals$

S
0
$Δ$
$2 Δ$

The correct answer is: 0

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$L t left parenthesis x rightwards arrow pi divided by 6 right parenthesis left parenthesis left parenthesis 3 s i n x minus √ 3 c o s x right parenthesis divided by left parenthesis 6 x minus pi right parenthesis right parenthesis equals$

$L t left parenthesis x rightwards arrow pi divided by 6 right parenthesis left parenthesis left parenthesis 3 s i n x minus √ 3 c o s x right parenthesis divided by left parenthesis 6 x minus pi right parenthesis right parenthesis equals$

For $x element of R L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis right parenthesis to the power of x equals$

For $x element of R L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis right parenthesis to the power of x equals$

$L i m left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x t a n 2 x minus 2 x t a n x right parenthesis divided by left parenthesis left parenthesis 1 minus c o s invisible function application 2 x right parenthesis squared right parenthesis equals$

$L i m left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x t a n 2 x minus 2 x t a n x right parenthesis divided by left parenthesis left parenthesis 1 minus c o s invisible function application 2 x right parenthesis squared right parenthesis equals$

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S0

In this question we have to use formula

The correct answer is: 0

In this question we have to find the value of Step1: Using formula of Solution of Triangle.By using Cosine RuleBy putting these values in the given expression.=>=>=>.Hence the value of the expression is .

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In $capital delta A B C comma sum left parenthesis left parenthesis b squared minus c squared right parenthesis right parenthesis divided by a c o s invisible function application A equals$

S
0
$Δ$
$2 Δ$

For $x element of R L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis right parenthesis to the power of x equals$

For $x element of R L t left parenthesis x rightwards arrow infinity right parenthesis left parenthesis left parenthesis x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis right parenthesis to the power of x equals$