First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{e^{\tan x} - e^{x}}{\tan x - x} =$

Moderate

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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