Mathematics

Problem

For

m>0

, define

p_m(x)= \begin{cases} |x|^{\,m}\sin\!\bigl(\tfrac{1}{x}\bigr), & x\ne 0,\\ 0, & x=0. \end{cases}

Determine all real values of

m

for which

p_m

is continuous at

x=0

but not differentiable at

x=0