F(X) = Sin 1 X for −1 ≤ X ≤ 1 Discuss the Applicability of Rolle'S Theorem for the Following Function on the Indicated Intervals ? - Mathematics

Question

f (x) = sin $\frac{1}{x}$ for −1 ≤ x ≤ 1 Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

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Solution

The given function is $f (x) = \sin \frac{1}{x}$ .

The domain of f is given to be $[- 1, 1]$ .

It is known that $lim_{x \to 0} \sin \frac{1}{x}$ does not exist.

Thus, $f (x)$ is discontinuous at x = 0 on $[- 1, 1]$ .

Hence, Rolle's theorem is not applicable for the given function.

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RD Sharma Mathematics [English] Class 12

Chapter 15 Mean Value Theorems
Exercise 15.1 | Q 1.3 | Page 8

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F(X) = Sin 1 X for −1 ≤ X ≤ 1 Discuss the Applicability of Rolle'S Theorem for the Following Function on the Indicated Intervals ? - Mathematics

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