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

# Lim X → π Sin X π − X - Mathematics

$\lim_{x \to \pi} \frac{\sin x}{\pi - x}$

#### Solution

$\lim_{x \to \pi} \frac{\sin x}{\pi - x}$
$= \lim_{h \to 0} \frac{\sin \left( \pi - h \right)}{\pi - \left( \pi - h \right)} \left[ \because \lim_{x \to a} f\left( x \right) = \lim_{h \to 0} f\left( a - h \right) \right]$
$= \lim_{h \to 0} \frac{\sin h}{h} \left[ \because \sin \left( \pi - 0 \right) = \sin 0 \right]$
$\Rightarrow 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.8 | Q 1 | Page 62