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Mean Value Theorems — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMean Value Theorems2 Marks
Question
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\sin\frac{1}{\text{x}}\text{ for}-1\leq\text{x}\leq1$
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Answer

The given function $\text{f}(\text{x})=\sin\frac{1}{\text{x}}$ The domain of f is given to be [-1, 1]. It is known that $\lim\limits_{\text{x}\rightarrow0}\sin\frac{1}{\text{x}}$ does not exist.Thus, f(x) is not discontinuos at x = 0 on [-1, 1].
Hence, Rolle's theorem is not applicable for the given function.

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