Q.The function $f(x) = \begin{cases} x^2 \sin(1/x) & x \ne 0 \ 0 & x = 0 \end{cases}$ is

continuous but not differentiable at

x=0

differentiable at

x=0

with

f'(0)=0

not continuous at

x=0

differentiable everywhere with

f'(0)=1

The correct solution involves applying the fundamental concept to derive the final value step by step...

Already a member? Login here

Q.The function f(x)={x2sin⁡(1/x)x≠0 0x=0f(x) = \begin{cases} x^2 \sin(1/x) & x \ne 0 \ 0 & x = 0 \end{cases}f(x)={x2sin(1/x)​x=0 0​x=0​ is