Limit Continuity And Differentiability Ques 41
- Let $f(x)=\left\{\begin{array}{lr}(x-1)^2 \sin \frac{1}{(x-1)}-|x|, & \text { if } x \neq 1 \\ -1, & \text { if } x=1\end{array}\right.$ be a real valued function.
Then, the set of points, where $f(x)$ is not differentiable, is …. .
(1981, 2M)
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Answer:
Correct Answer: 41.( $x=0$)
Solution: Given, $f(x)=\left\{\begin{array}{cc}(x-1)^2 \sin \frac{1}{(x-1)}-|x|, & \text { if } x \neq 1 \\ -1, & \text { if } x=1\end{array}\right.$
As, $\quad f(x)=\left\{\begin{array}{cc}(x-1)^2 \sin \frac{1}{(x-1)}-x, & 0 \leq x-\{1\} \\ (x-1)^2 \sin \frac{1}{(x-1)}+x, & x<0 \\ -1, & x=1\end{array}\right.$
Here, $f(x)$ is not differentiable at $x=0$ due to $|x|$.
Thus, $f(x)$ is not differentiable at $x=0$.
BETA
