Saved Bookmarks
| 1. |
\( \lim _{x \rightarrow 0}\left(1+\tan ^{2} x\right)^{\frac{1}{x^{2}}} \) is e \( \frac{1}{e} \) 0 1 |
|
Answer» \(\lim\limits_{x \to 0}\)(1 + tan2x)\(\frac1{x^2}\) (1\(\infty\) = case) = Exp {\(\lim\limits_{x \to 0}\)(1 + tan2x - 1) \(\frac1{x^2}\)} = Exp {\(\lim\limits_{x \to 0}\) \(\frac{tan^2x}{x^2}\)} = Exp {\(\lim\limits_{x \to 0}\)\((\frac{tan y}x)^2\)} = e (∵ \(\lim\limits_{x \to 0}\)\(\frac{tan x}x=1\)) |
|