COMEDK · Maths · 16. Limits
\(\lim _{x \rightarrow 1} \frac{\tan \left(x^{2}-1\right)}{x-1}\) is equal to
- A \(\frac{1}{2}\)
- B 2
- C \(\frac{-1}{2}\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} \lim _{x \rightarrow 1} & \frac{\tan \left(x^{2}-1\right)}{x-1} \\ &=\lim _{x \rightarrow 1} \frac{\sec ^{2}\left(x^{2}-1\right) \cdot 2 x}{1} \quad \text { [using L'Hospital Rule] } \\ &=2 \sec ^{2} 0=2 \end{aligned} \]
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