Let f(x)= cases x^p ( 1 x ), & x 0 0, & x=0 cases Then is continuous but not…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)=\begin{cases}x^p\sin\left(\frac{1}{x}\right), & x\ne0\\0, & x=0\end{cases}

Then

f(x)

is continuous but not differentiable at

x=0

if (a)

0<p\le1

(b)

1\le p<\infty

(c)

-\infty<p<0

(d)

p=0