JEE Mains · Maths · STD 11 - 12. limits
\(\lim \limits_{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}\) is equal to
- A \(2\)
- B \(e\)
- C \(1\)
- D \(e^{2}\)
Answer & Solution
Correct Answer
(D) \(e^{2}\)
Step-by-step Solution
Detailed explanation
\(\lim \limits_{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}\) \(=\lim \limits_{x \rightarrow 0} \frac{1}{x}\left\{\tan \left(\frac{\pi}{4}+x\right)-1\right\}\) \(=\lim \limits_{x \rightarrow 0}\left(\frac{1+\tan x-1+\tan x}{x(1-\tan x)}\right)\)…
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