Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

Lim X → 0 E Sin X − 1 X - Mathematics

$\lim_{x \to 0} \frac{e\sin x - 1}{x}$

Solution

$\lim_{x \to 0} \left[ \frac{e\sin x - 1}{x} \right]$

$= \lim_{x \to 0} \left[ \frac{e\sin x - 1}{\sin x} \times \frac{\sin x}{x} \right]$

x → 0
∴ sin x → 0

Let y=sin

x → 0
∴ y → 0

$\Rightarrow \lim_{y \to 0} \left( \frac{e^y - 1}{y} \right) \times \lim_{x \to 0} \left( \frac{\sin x}{x} \right)$
$= 1 \times 1$

Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 17 | Page 71