Search any question & find its solution
Question:
Answered & Verified by Expert
$\lim _{x \rightarrow 1} \frac{\tan \left(x^{2}-1\right)}{x-1}$ is equal to
Options:
Solution:
2533 Upvotes
Verified Answer
The correct answer is:
2
We have,
$$
\begin{aligned}
\lim _{x \rightarrow 1} & \frac{\tan \left(x^{2}-1\right)}{x-1} \\
&=\lim _{x \rightarrow 1} \frac{\sec ^{2}\left(x^{2}-1\right) \cdot 2 x}{1} \quad \text { [using L'Hospital Rule] } \\
&=2 \sec ^{2} 0=2
\end{aligned}
$$
$$
\begin{aligned}
\lim _{x \rightarrow 1} & \frac{\tan \left(x^{2}-1\right)}{x-1} \\
&=\lim _{x \rightarrow 1} \frac{\sec ^{2}\left(x^{2}-1\right) \cdot 2 x}{1} \quad \text { [using L'Hospital Rule] } \\
&=2 \sec ^{2} 0=2
\end{aligned}
$$
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.