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Question
`\lim_{x \to 0} \frac{e^x - e^\sin x}{x - \sin x}`
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Solution
`\lim_{x \to 0} \left[ \frac{e^x - e^\sin x}{x - \sin x} \right]`
` = \lim_{x \to 0} \left[ \frac{e^\sin x \left[ \frac{e^x}{e^\sin x} - 1 \right]}{x - \sin x} \right]`
` = \lim_{x \to 0} e^\sin x \left[ \frac{e^{x - \sin x} - 1}{x - \sin x} \right]`
` = e^\sin 0 `
\[ = 1\]
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