Lim X → π 2 E Cos X − 1 Cos X - Mathematics

\lim_{x \to \pi/2} \frac{e^\cos x - 1}{\cos x}

Solution

$\lim_{x \to \frac{\pi}{2}} \left[ \frac{e^{cos x} - 1}{\cos x} \right]$
$\text{ If } x \to \frac{\pi}{2}, \text{ then } \cos x \to 0 .$
$\text{ Let } y = \cos x$
$= \lim_{y \to 0} \left[ \frac{e^y - 1}{y} \right]$
$= 1$

Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 32 | Page 72