limx→0 etan⁡x−extan⁡x−x= - Infinity Learn by Sri Chaitanya

A
1
B
$e$
C
$e - 1$
D
0

Solution:

We have,

$\begin{array}{l} lim_{x \to 0} \frac{e^{\tan x} - e^{x}}{\tan x - x} = lim_{x \to 0} \frac{e^{x} \{e^{\tan x - x} - 1\}}{\tan x - x} \\ = lim_{x \to 0} e^{x} \times lim_{x \to 0} \frac{e^{\tan x - x} - 1}{\tan x - x} = e^{0} \times 1 = 1 \end{array}$

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