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  • <img alt="\lim _{x \rightarrow 0} \frac{\int_0^{x^2} \cos t^2 d t}{x \sin x}=\ldots \ldots" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%20_%7Bx%20%5Crightarrow%200%7D%20%5Cfrac%7B%5

\lim _{x \rightarrow 0} \frac{\int_0^{x^2} \cos t^2 d t}{x \sin x}=\ldots \ldots

 

Option: 1

0


Option: 2

1


Option: 3

-1

 


Option: 4

2


Answers (1)

best_answer

\text { Form }\left(\frac{0}{0}\right)

Applying L' Hospital's rule 

Then           \lim _{x \rightarrow 0} \frac{\cos x^4 \cdot 2 x}{x \cos x+\sin x \cdot 1}

                   \begin{aligned} & =\lim _{x \rightarrow 0} \frac{2 \cos x^4}{\cos x+\left(\frac{\sin x}{x}\right)} \\ \\& =\frac{2 \times 1}{1+1}=1 \end{aligned}

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manish

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