Consider the function g(x)= cases |x-1| ,x-1 , , & x 1, 0, & x=1

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the function

g(x)= \begin{cases} \dfrac{|x-1|}{\,x-1\,}, & x\neq1,\\ 0, & x=1. \end{cases}

At which of the following point(s), if any, is

g

not continuous? (a) At

x=1

and

x=0

(b) Only at

x=1

x

(d) At no point (continuous everywhere)