Turito Academy

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In <img src="data:image/png;base64,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" class="Wirisformula" alt="triangle A B C comma sum a cos invisible function application A equals" width="145" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#9651;«/mo»«mi»A«/mi»«mi»B«/mi»«mi»C«/mi»«mo»,«/mo»«mo»§#8721;«/mo»«mi»a«/mi»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»A«/mi»«mo»=«/mo»«/math»'/>

Solution for the question - in /_\abc,sum ac 05 a= 2 reosacos bcos '/> 285 in asingsin '/> 4r5 a. asinbsinl '/> 4 reo5ac05bcos '/>

In /_\abc,sum ac 05 a= -Turito

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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

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,iVBORw0KGgoAAAANSUhEUgAAACAAAAARCAYAAAC8XK78AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAASFJREFUeNpjYKAMZAFxBwnqO6B6CAImIBZH4v8H4rtoavSA+DgZjj4K1YsTeADxOyi+AsQsUAcsxGKQARb9akBcC8QXcJhvDMSHcVkOsuwpksFaSCEQjqTOAOoAbGAxEKdB9eACh6EOwQBBQLwcizjIMEkkfhcQ5xAIanwOyMOVduqBuByLOHr87wBiWwocYAnEe9EF10E1wXAkkpw5mtpPQMxGgQPYoGZggBtALEtESv5DhJr/BOR/Yct634jMSjRxACiY9xPpAJpEASjO5xPpgN1AbE3tRDgJmn+JAZRmwxyoGRi5wItIB+AriIhxANaCCFT0cpBQph/HUab/x4IJFsWiQPycxEqFapXRBGj+7yDDsAwS9XVhS2fG0DpgQAAANWxLpEx7IK4AAABxdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmY8L21pPjxtbz4nPC9tbz48bW8+KDwvbW8+PG1uPjE8L21uPjxtbz4pPC9tbz48L21hdGg+3kWY4QAAAABJRU5ErkJggg==" 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,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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»'/> =&gt; <img src="data:image/png;base64,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" 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,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" 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,iVBORw0KGgoAAAANSUhEUgAAAHYAAAATCAYAAABFnvn4AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAutJREFUeNrtWUFoU0EQ/YQSihRBRDyICKWIiEigiEgp4qWUUqQEcigexIuIFBEvHop4LT0FD0IR6TFQQvEgIogEKaF4EREPUhBPIr3k4KF8QqDOwot+tzPb2Sb7v/n2waNkO5vu+zN/ZnYaRYewsUv8ePgY8unYxf9N9F3ikof9EvYMmmPP5lV7gXjSWrtI3DzAdzWx91+FrfUDY5ML7dPEFviZOJQ4ZMmKbIlJjBM3Apxzglgn/iS2URdv9Ekr56CStXaU+JT4HlzBWhrarxFfEXeIMXGLWCUelzYYYd8TIs7jZwni7JSlxQZE9hPviPPEkcRZm1jTQNJqg9Nu8JZ4PfF5FmtpaG8Qy8Sidc7X0gZjXGPWl4kLPTj2nmd9OijOED8pbSWtGu0V4hPGtsoEVlraI2QvFo+JD5l1EwmTPTj2ihDNIRAr7SStGu2mBEwJKbKekfZR4hfuF+tWnZy3IqHYg2OLjmjaVdAngJoKO5dW7i2wtbeYta7O7ZS1m8bvFursjGRkPH6aWe8Ih2rj0KaQP0jUOw7twBE7jCZmQmkvadVo73jqDKHdDoD7rrZ/x0NcsgkxzcEjPKxzGTj2GPGFkB59tfbq2DgD7XMI6qucwWV0W9p0xGEK3WqaqXgUTh3zeBgurRrt28LzGM4gFXcxAufugakzq8KmNx4pLk6xeTLZ4RnxiOc+l1aN9jruwFxgZ9U8iY2jad9ve7T8HC4QvzLrC/iOfsI0DWuOoYILLq0a7WUElI1VphELoT0SpmNbUqc443FJX0c0FsBpOLWc0iX9paOeJ1FDSptTatUOKBpoWIaQbheFMhRqOFPB3y7gmvWNeJMzbqFGSNiM/p57VhAhHew1b88lZl+osZq2LnGO3U/rftq7TctzpD/TiK0wt4JQ2icR2DHYwORrD04Qfyhe9UEdhNcSb6hGay60V3FN0Yy97niOx5Y9alkomFTaHfD7aB147eNCXcwLTkV//i2Xd62/8QvGa/h1p1Py9gAAANh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPig8L21vPjxtbj41PC9tbj48bW8+KTwvbW8+PG1vPj08L21vPjxtbj4yPC9tbj48bW8+LDwvbW8+PG1zdXA+PG1pPmY8L21pPjxtbz4nPC9tbz48L21zdXA+PG1vPig8L21vPjxtbj4wPC9tbj48bW8+KTwvbW8+PG1vPj08L21vPjxtbj4zPC9tbj48L21hdGg+dmgyPgAAAABJRU5ErkJggg==" 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,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" 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,iVBORw0KGgoAAAANSUhEUgAAAXoAAAATCAYAAACeLMa2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABZVJREFUeNrtXE1IVUEUHkREJAIRkYgQREJaiNBCHhLRRiRC4kELaRWBRIi0axHiVlqERAQSIREhSEgLiSAiRCSiiIgW4aaVhBsXEvIQ4TUHj/S6zZmfO2fm3fecD87CuePM+fnO3Pm7T4iEhPqjirIvZUNKf3JJ4kBySUJCc6JFym0pX5IrEgeSK4oLCNBcg+g6h/py2dJIthcdFYc4FY3TKn1dbRjCWe1x5mWloONCM/LNCYNSPjQYmTZQbxdbYMbR0wS2FxUXpaxZxol7JskVV5W+LjY8kXL9GPNSxYEijAtNxbc9VCJPZ0OM7fnipJTHUj6iLGBZLc5LWXewZUzKDsp3Ka1E/REpL6XsisM9x69E4sb2kateHHCx7RT6ss8yTlzgjqtKX1sbuqX8JHzmy8t65SQHBzhxVsoMxk9Yxq8efPPRV2sDHIB80yjYTywpqaWmqb2QeCdlvObvK1iWxTo6xWQLBGOrJhDnNPVhNjIh5URN3Q0sq6ePXPTigIttQOZVTHRhEScuhIqrSl8bG+5hUtvmmIv+9chJTg5w4bmUSXF4+CsKzDdffUkbrkpZ0jRWlvJCUX5fylSO9kLhmpSHivJ5RVJOi3/3xChbyoQtVP0segnCc/io6vG/vY6J79KXrW2Q2K8VKy5dnLgQKq4qfU02tOBsvttBH1f9Y+ckJwe4+V9tML656kvaMCvlLtHQrPh7BaqaqfdGygVNe11SHkjZxuXKdE4nzQi7a1ewvB5VlF/CZ7UoZWb6JluyoOqrUAnko6on+SqB+rK1DRJ8wNBWiViR+SJUXFX6mmyASchT4hkXL7lzMiYHYg70ReSbq76kDcv4BqZAPYc9yzai/iwuIcZxxnIaE6Mjh5OWsC/TVsMOoU8bEi1btmuwZSXzkpuwsF0ViI1APvIZ6EuaJaNvX7a2VRUiDHHiQMi4qvQ12aDbLuDiJXdOxuRAzIG+iHxz1Ze0YRODQOEHLlWzOCDqb+Ke2wnFQNyVw1FwSv0ZDYabCe1EvQNNG/uGsgON7Wcc+zoC6AkHwiOBfJSX6Dq9OPrijv9+gIEoVFxtuFaLIcMLl4uX3DGJzYFYA30R+ZZH3//K4E37W9MIPN9zIOFRe9lZQqumHerNTslyjoG+kmOgd7W9Fp1SXhFbSSF9JDz04ugrr215Es9HxxBxzTPQU1cqOXkZm28hOMDFf5+Bvh58Yxvoh6W81zQCz9cclpXDxP5QydCP7Yx+QbPU2SaetefcutH5Rrfk6sPBoF/jUw4fuc5oTHpx9MUd/xBL6VBxdV1K665UcvIyRE7G5ECjb93k5Rvr1g3sFy1qGoLnz4hnbxXLV6o9Uz862O7Rw4HrmKJ8VJgPY11soeoDBnCW1mHwKYePXIhuoxdHX9zxD3E4FiqulL6UDdSVSsHMyxA5GZMDMQf6ovDNR1+lDXAd8YamIbiaSF3/UV0NotqD8ps5HWV766aMyZjFouIlMYX6m2yZdLC9B7eVWg16cvnIlui2enH0xR3/bJw4ECqulL6qMt2VSsHMyxA5GZMDMQf6IvDNV1+lDSvELPgIjwR99Ut1kATtXVbUpcq5AUukO5iUbThrUm092XwwpdNZVX9V2F0V4/KRLdFt9eLoizv+IT5gCRVXSl9Vme5KpWDmZeycjNVfiIG+CHzz1Vdpw46gDxZgoIQvuLZq/s4CfqNhMNOe6lYMVc6NTkwgOHyFAxDY08+e/FOfCdvaQtW3PaSJ7SPfwysXcNoW6pP0UHF1+STdZUDx5WVsvtV7DHDJgyLyzUffYD/j0Kw/agZL6l9NaHszxMkHIePq+6NmNvokXia+heYbiVuicX4SFfauJg22fBKH917nmsz2RoIpTnkwHzCuKn05bUi8THyLybdjAVj+lJMbUlyT/gmNHK8/jZHQ8bCr5KoAAAH6dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPkw8L21pPjxtaT50PC9taT48bW8+KDwvbW8+PG1pPmg8L21pPjxtbz4mI3gyMTkyOzwvbW8+PG1uPjA8L21uPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPmY8L21pPjxtbz4oPC9tbz48bW4+MjwvbW4+PG1pPmg8L21pPjxtbz4rPC9tbz48bW4+MjwvbW4+PG1vPis8L21vPjxtc3VwPjxtaT5oPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4pPC9tbz48bW8+LTwvbW8+PG1pPmY8L21pPjxtbz4oPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjxtbz4pPC9tbz48bW8+LzwvbW8+PG1vPig8L21vPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPmg8L21pPjxtbz4tPC9tbz48bXN1cD48bWk+aDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjE8L21uPjxtbz4pPC9tbz48bW8+LTwvbW8+PG1pPmY8L21pPjxtbz4oPC9tbz48bW4+MTwvbW4+PG1vPik8L21vPjxtbz4pPC9tbz48L21hdGg+HqxsJQAAAABJRU5ErkJggg==" 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,iVBORw0KGgoAAAANSUhEUgAAAQ4AAAATCAYAAABhjuNUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA5lJREFUeNrtW1+EVUEYH7lWkkjWSnJJsrJySbKS3pIesvbt6jFWsnroZR/WShJrn5JEekhWLrlWDyuRJGslspIe0kt6uLIu+5Bcay3bN+d+d/cY35ydOefM3fnmnB8/u+b82fP7zTez33xnjhAlVGwBv5Y2lMgplkoUqLOnSxtKlBNHfrgFnLU4fxav4dbZpwqqvcj97gLrRfNzH3BIaTsD/JTiXst4LRetK8Q5oWo3QZG1Z8XfIvl5BbiG/A6sxB68luJ+Z4FLDp7zArCJnbOBdYnrOWmlOs0n7T3IzGhGuK3J+Kqdg39tBn7mMY6igdOKCTuNP2soOC2WUHie+AisAw/GnnUZ27JoVeGj9h7mgRMO19I+a+fgX4uBn1nHUYRxYINonwNOZni425ZrurSoAr9l1MpRu6vA59Lvvvr3qwDjKMJd4BTR/hZ4UVMfuAdcjaU5VeK8UeD7PgXBekatHLWnCfwDGMht9Eymq48VTzj1u4/+FWEciQU0sMe6UuQZIK5ZBD4CHkbxr4BjxHkDmkKRUP6mjqYYNUwFk7Sq4KDdNvArmKJO4e+Sd4CbigYu/d7vicPUvy2GsWQzjrbxA3icaN8k2uooMI4XwKuae2847vz9wM9Y7MmilaN228CXBcEHRPtP4FFm2n32rwjjKJrpOhaCP+DMpBZaqnsgWM7Ur4GXc9DKTXuawP8DPEJ48o+Z9r3K2Ez9C30cRTiPIkzT9Q6aZWKcyxTrBIo9mZNWTtrTBL7utR7lCQft/Z54bfwLfRxtp0zPNcfeEamL+o5aHl9JWDO5KOoMA59hoSovrVy0pw18+TZp3tATDtp99i/0cRRBFmcmNMeo10gtXA/F131NzfWTeI88MYRrw0rOWjlozxL41wT9GloOhhsMtfvsX+jjKMJCQkGG2rhyH/gUUyu5HnsJfKO53sXGlUWcKXdDAwNjzFArB+2mgU9pPyS6r/1qMX1NDOBLDLX77F/o4yjCmjLzqZD769W98tM4W83gtavEjV1tlTVdy1GCd9Pqu/YkD0w6W/7X/I2Fti9YDGsra23ftXPxL+RxJAZFt1KcBJOPcwaJNh8+zmnEMgwTraFq12FE6HfRctbug3/BxtJD0d3TYLKV9aaw2/I6Z1FLcAWZHvY+YLPRGpr2eCHsidjZb3AOg3I4MO0++RdkLMkUaFyEi2Ni57P50LUmae9Bfswki8PylV8H19MjokTpn4UX/wHISfjn7Z+jGwAAAY90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ZjwvbWk+PG1vPig8L21vPjxtaT5hPC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtbj4yPC9tbj48bW8+LDwvbW8+PG1zdXA+PG1pPmY8L21pPjxtbz4nPC9tbz48L21zdXA+PG1vPig8L21vPjxtaT5hPC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtbj4xPC9tbj48bW8+LDwvbW8+PG1pPmc8L21pPjxtbz4oPC9tbz48bWk+YTwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bW8+LTwvbW8+PG1uPjE8L21uPjxtbz4sPC9tbz48bXN1cD48bWk+ZzwvbWk+PG1vPiE8L21vPjwvbXN1cD48bW8+KDwvbW8+PG1pPmE8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1uPjI8L21uPjxtbz4sPC9tbz48L21hdGg+M01CqwAAAABJRU5ErkJggg==" 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,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" 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

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In $triangle A B C comma sum a cos invisible function application A equals$

$4 R \cos A \cos B \cos C$
$4 R \sin A \sin B \sin C$
$2 R \sin A \sin B \sin C$
$2 R \cos A \cos B \cos C$

The correct answer is: $4 R sin invisible function application A sin invisible function application B sin invisible function application C$

Related Questions to study

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

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

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

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

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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In

In

If is finite then the values of a,b are respectively

If is finite then the values of a,b are respectively

If then

If then

If be a positive increasing function with then

If be a positive increasing function with then

If and then is

If and then is

is

is

For

For

, given that and

, given that and

If then the value of is,

If then the value of is,

If then has the value

If then has the value

If then is

If then is

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In $triangle A B C comma sum a cos invisible function application A equals$

The correct answer is: $4 R sin invisible function application A sin invisible function application B sin invisible function application C$

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

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

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