Question 12 Marks
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\sin\frac{1}{\text{x}}\text{ for}-1\leq\text{x}\leq1$
$\text{f}(\text{x})=\sin\frac{1}{\text{x}}\text{ for}-1\leq\text{x}\leq1$
Answer
View full question & 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.