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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\text{e}^{-\cos\text{x}}-1}{-\cos\text{x}}$
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Answer

$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\text{e}^{-\cos\text{x}}-1}{-\cos\text{x}}$ Let $\text{ x}-\frac{\pi}{2}=\text{h}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{\text{e}^{-\sin\text{h}}-1}{-\sin\text{h}}$ $=\lim\limits_{\sin\text{h}\rightarrow0}\frac{\text{e}^{-\sin\text{h}}-1}{-\sin\text{h}}$ $=1$

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