Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Lim X → 0 E Sin X − 1 X - Mathematics

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

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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 

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

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APPEARS IN

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