Consider the function g(x)= cases |x| x , & x 0, [2pt] 1, & x=0

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

Problem

Consider the function

g(x)=\begin{cases} \dfrac{|x|}{x}, & x\neq 0,\\[2pt] 1, & x=0. \end{cases}

g

continuous at

x=0

? Give a brief reason for your answer.