Search any question & find its solution
Question:
Answered & Verified by Expert
The value of the limit
$$
\lim _{x \rightarrow 0}\left(\frac{x}{\sin x}\right)^{6 / x^{2}}
$$
is
Options:
$$
\lim _{x \rightarrow 0}\left(\frac{x}{\sin x}\right)^{6 / x^{2}}
$$
is
Solution:
1502 Upvotes
Verified Answer
The correct answer is:
e
$\lim _{x \rightarrow 0}\left(\frac{x}{\sin x}\right)^{6 / x^{2}}$
$e^{\lim _{x \rightarrow 0} \frac{6}{x^{2}}\left(\frac{x-\sin x}{\sin }\right)}$
$\lim _{x \rightarrow 0} \frac{6}{x^{2}}\left(\frac{x-\left(x-\frac{x^{3}}{3}\right)}{x}\right)$
$=\mathrm{e}$
$e^{\lim _{x \rightarrow 0} \frac{6}{x^{2}}\left(\frac{x-\sin x}{\sin }\right)}$
$\lim _{x \rightarrow 0} \frac{6}{x^{2}}\left(\frac{x-\left(x-\frac{x^{3}}{3}\right)}{x}\right)$
$=\mathrm{e}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.