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