Turito Academy

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Solution for the question - 4(x rarr2)log_(1)0[x^(6)+sqrt({:(x^(2)+1292)]):} 6021

4(x rarr2)log_(1)0[x^(6)+sqrt({:(x^(2)+1292)]):} -Turito

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Solution for the question - (t(x rarr0)(1-cos x)//(x rarr0)1//x^(2):} 1//2 '/>210

(t(x rarr0)(1-cos x)//(x rarr0)1//x^(2):} -Turito

Solution for the question - 4(x rarr0)(3sin x^(0)-sin 3x^(8))//x^(3) 4(pi//180)^(3) '/> (pi//180)^(3) '/>10

4(x rarr0)(3sin x^(0)-sin 3x^(8))//x^(3) -Turito

Solution for the question - u(x rarr0)((1+x)(1//5)-(1-x)(1//2))//x 0141//4 '/>

U(x rarr0)((1+x)(1//5)-(1-x)(1//2))//x -Turito

Solution for the question - l^()(x rarr0)(sin(picos^(2)x))//x^(2) ji '/> /_jl '/>01

L^()(x rarr0)(sin(picos^(2)x))//x^(2) -Turito

Solution for the question - l^()(x rarr0)(e^(x)-e^(3))//(x rarr0) e^(2) '/>01e

L^()(x rarr0)(e^(x)-e^(3))//(x rarr0) -Turito

Solution for the question - t(x rarr0)(e^(3)x-e^(3))//x 301e^(x) '/>

T(x rarr0)(e^(3)x-e^(3))//x -Turito

Solution for the question - 4(x rarr0)(e^(7)x-1)//7x e017

4(x rarr0)(e^(7)x-1)//7x -Turito

Solution for the question - (x rarr0)(sin x)//(x cos x) none of thesea01

[(x rarr0)(sin x)//(x cos x) -Turito

Solution for the question - {:4(x rarr3)(x-3)//sqrt(()|x^(2)-9|) 9031

{:4(x rarr3)(x-3)//sqrt(()|x^(2)-9|) -Turito

Solution for the question - l^()(x rarr0)x^(2)cos 2//x none of thesedoes not exist01

L^()(x rarr0)x^(2)cos 2//x -Turito

The given function is <img src="data:image/png;base64,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" class="Wirisformula" alt="f open parentheses x close parentheses equals fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1" width="142" height="37" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«/mrow»«mi»x«/mi»«/mfrac»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math»'/> We have to find the limit of the function. <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow 0 to the power of plus of f open parentheses x close parentheses equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1" width="223" height="42" 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»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mfrac»«mrow»«mn»2«/mn»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«/mrow»«mi»x«/mi»«/mfrac»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math»'/> |x| can have two values, positive and negative. |x| = x          x&gt;0 |x| = -x        x&lt;0 In this care the limit is right hand limit tending to zero. So, x&gt;0 |x| = x <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow 0 of f open parentheses x close parentheses equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1
space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 x over denominator x end fraction plus x space plus space 1
space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of 2 space plus space x space plus space 1
space space space space space space space space space space space space space space equals space 2 space plus space 0 space plus space 1
space space space space space space space space space space space space space space space equals space 3
" width="214" height="180" style="vertical-align:-78px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mfrac»«mrow»«mn»2«/mn»«mo»|«/mo»«mi»x«/mi»«mo»|«/mo»«/mrow»«mi»x«/mi»«/mfrac»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mfrac»«mrow»«mn»2«/mn»«mi»x«/mi»«/mrow»«mi»x«/mi»«/mfrac»«mo»+«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«msup»«mn»0«/mn»«mo»+«/mo»«/msup»«/mrow»«/munder»«mn»2«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mspace linebreak=¨newline¨/»«/math»'/> The final value is 3.

Solution for the question - l(x rarr d)((2|x|)//x+x+1) 0213

L(x rarr d)((2|x|)//x+x+1) -Turito

Solution for the question - {:l_(()^(t)rarr2)(|x-2|)//(x-2) 201-1

{:l_(()^(t)rarr2)(|x-2|)//(x-2) -Turito

Solution for the question - {:l_(()x rarr0)(1-cos mx)//(1-cos nx),n!=0 0m^(2)n^(2) '/> m^(2)//n^(2) '/> n^(2)//m^(2) '/>

{:l_(()x rarr0)(1-cos mx)//(1-cos nx),n!=0 -Turito

Solution for the question - u(x rarr0)(1-cos 2mx)//(sin^(2)nx)(m,n in z) (2n^(2))//mn^(2) '/> n^(2)//m^(2) '/> m^(2)//n^(2) '/> (2m^(2))//n^(2) '/>

U(x rarr0)(1-cos 2mx)//(sin^(2)nx)(m,n in z) -Turito

Solution for the question - {:delta_(()x rarr0)(x tan 2x-2x tan x)//((1-cos 2x)^(2)) 201//2 '/>1

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