Let be the function defined by g(x)= cases |x| x ,&x 0 2,&x=0

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

Problem

Let

g

be the function defined by

g(x)=\begin{cases}\dfrac{|x|}{x},&x\neq0\\2,&x=0.\end{cases}

Determine

\displaystyle\lim_{x\to0}g(x)

, or state that the limit does not exist.