First slide

Introduction to limits

Question

The value of $lim_{x \to 2} \frac{e^{3 x - 6} - 1}{\sin (2 - x)},$ is

Moderate

A

$3 / 2$
B

3
C

$- 3$
D

$- 1$

Solution

We have,
$\begin{array}{l} lim_{x \to 2} \frac{e^{3 x - 6} - 1}{\sin (2 - x)} \\ = lim_{x \to 2} \frac{e^{3 (x - 2)} - 1}{3 (x - 2)} \times \frac{- 3 (2 - x)}{\sin (2 - x)} = 1 \times - 3 = - 3 \end{array}$

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