Define for and

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define

g(x)=x^{2}\sin\!\left(\tfrac{1}{x}\right)

for

x\neq 0

and

g(0)=0

. Without directly evaluating

g(0)

, determine

\displaystyle\lim_{x\to 0}g(x)

, given that

g

is differentiable at

x=0