For , define p_m(x)= cases |x|^ ,m ! ( 1 x ), & x 0, 0, & x=0. cases Determine all…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

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