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