If lim x rightarrow 0 (tan x/x ) frac 1 x 2 =p , then 96 log e p is equal to

Mathematics · Limits, Continuity and Differentiability

JEE Main 2025 — 3 April, Evening Shift — Question 43

If $\lim _{x \rightarrow 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^{2}}}=p$ , then $96 \log _{e} p$ is equal to

Numerical answer — enter this value.

$\lim _{x \rightarrow 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^{2}}}=p$

$\because$ Form: $1^{\infty}$

\begin{aligned} \Rightarrow & \left.p=e^{\lim _{x \rightarrow 0}\left(\frac{\tan x}{x} 1\right.}\right) \frac{1}{x^{2}} \\& =e^{\lim _{x \rightarrow 0}\left(\frac{\tan x-x}{x^{3}}\right)} \end{aligned}

$\Rightarrow \quad \log _{e} p=\frac{1}{3}$

$\Rightarrow{96 \log _{\mathrm{e}} p=32}$

Answer key and solution verified before publishing.

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