Question

limit class 11
lim(x -> sinx) (e^x - e^ sinx )/(x - sinx) ​

Answer 1

Appropriate Question:

$\displaystyle \tt\lim \limits_{x \to 0} \frac{ {e}^{x} - {e}^{ \sin(x) } }{ x - \sin(x) }$

Step-by-step explanation:

We have,

$\displaystyle \tt \lim \limits_{ x \to 0} \frac{ {e}^{x} - {e}^{ \sin(x) } }{x - \sin(x) }$

$\displaystyle = \tt \lim \limits_{ x \to 0} \frac{ {e}^{ \sin(x)} ({e}^{x - \sin(x)} - 1)}{x - \sin(x) }$

${\displaystyle = \tt \lim \limits_{ x \to0} \frac{ {e}^{x - \sin(x)} - 1}{x - \sin(x) } \cdot {e}^{ \sin(x)}}$

Using standard limit, we get:

${\displaystyle = \tt \lim \limits_{ x\to0} (1) \cdot {e}^{ \sin(x)}}$

${\displaystyle = \tt {e}^{ \sin(0)}}$

${\displaystyle = \tt {e}^0}$

${\displaystyle = \tt {e}^1}$