Let f(x)= cases x^p 1 x ,&x 0 0,&x=0 cases

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

Problem

Let

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

Then

f(x)

is continuous but not differentiable at

x=0

if (a)

0<p\leq1

(b)

1\leq p<\infty

(c)

-\infty<p<0

(d)

p=0