Mathematics - Limits Question with Solution | TestHub

$P={\lim }_{x\to 0}{\left(\frac{\tan x}{x}\right)}^{\frac{1}{x^2}}$
$\Rightarrow \mathrm{P}={\mathrm{e}}^{{\lim }_{\mathrm{x}\to 0}\left(\frac{\tan x-\mathrm{x}}{{\mathrm{x}}^3}\right)}$
$={\mathrm{e}}^{{\lim }_{x\to 0}\frac{\left(x+\frac{x^3}{3}+\frac{2x^5}{15}+\dots ..-x\right)}{x^3}}$
$=e^{1/3}$
$\therefore 96{\log }_{\mathrm{e}}^{\mathrm{p}}=96\times \frac{1}{3}=32$