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Lim X → π 2 E Cos X − 1 Cos X - Mathematics

`\lim_{x \to \pi/2} \frac{e^\cos x - 1}{\cos x}`

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Solution

\[\lim_{x \to \frac{\pi}{2}} \left[ \frac{e^{cos x} - 1}{\cos x} \right]\]
\[\text{ If } x \to \frac{\pi}{2}, \text{ then } \cos x \to 0 . \]
\[\text{ Let } y = \cos x\]
\[ = \lim_{y \to 0} \left[ \frac{e^y - 1}{y} \right]\]
\[ = 1\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 32 | Page 72
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