Question

Lt
P- sin
X Х
이
Yo - J
e
(-x) 2
12​

Answer 1

Step-by-step explanation:

We have,

$\lim_{x \rarr\pi } \frac{p - \sin( \frac{x}{2} ) }{(\pi - x)^{2} }$

Let y = x - π

=> x = y + π

$\lim_{y \rarr0 } \frac{p - \sin( \frac{y + \pi}{2} ) }{ {y}^{2} }$

since, this ia 0/0 form, so, using l'hospital's rule

$\lim_{x \rarr0 } \frac{ - \cos( \frac{y + \pi}{2} ) \times \frac{1}{2} }{2y}$

$\lim_{y\rarr0 } \frac{ \sin( \frac{y + \pi}{2} ) \times \frac{1}{4} }{2}$

$= \frac{1}{4 \times 2}$

$= \frac{1}{8}$