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Differentiation question

2024 · 6 Apr · Shift 1 · Q43

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JEE Main
Mathematics
Differentiation
2024 · 6 Apr · Shift 1 · Q43

Differentiation question

2024 · 6 Apr · Shift 1 · Q43

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R}

be a differentiable function such that

f^{\prime}(1)=\lim_{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right)

. Then

\lim_{a \rightarrow \infty} \frac{a(a+1)}{2} \tan ^{-1}\left(\frac{1}{a}\right)+a^2-2 \log _e a

is equal to

A
$\frac{5}{2}+\frac{\pi}{8}$
B
$\frac{3}{8}+\frac{\pi}{4}$
C
$\frac{3}{4}+\frac{\pi}{8}$
D
$\frac{3}{2}+\frac{\pi}{4}$

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