Let $f(x) = \begin{cases} x^p \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$ th…

Mathematics

Problem

Let

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

then

f(x)

is continuous but not differentiable at

x = 0

if (a)

0 < p \leq 1

(b)

1 \leq p < \infty

(c)

-\infty < p < 0

(d)

p = 0