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  • If <img alt="\mathrm{ \lim _{y \rightarrow \infty} \frac{\int_1^y\left[\tan ^{-1} x\right] d x}{\int_1^y\left[1+\frac{1}{x}\right] d x} }" src="https://entrancecorner.oncodecogs.com/gif.latex?

If \mathrm{ \lim _{y \rightarrow \infty} \frac{\int_1^y\left[\tan ^{-1} x\right] d x}{\int_1^y\left[1+\frac{1}{x}\right] d x} } (where [.] denotes the greatest integer function) is

Option: 1

\infty


Option: 2

1


Option: 3

\tan 1


Option: 4

does not exist 


Answers (1)

best_answer

\mathrm{\frac{\lim _{y \rightarrow \infty} \int_1^y\left[\tan ^{-1} x\right] d x}{\lim _{y \rightarrow \infty} \int_1^y\left[1+\frac{1}{x}\right] d x}=\lim _{y \rightarrow \infty} \frac{y-\tan 1}{y-1}=1}

Posted by

Ajit Kumar Dubey

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