Consider the function h(x)= cases |x| x , & x 0

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

Problem

Consider the function

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

Which of the following statements about the continuity of

h

x=0

is correct? (a) Continuous if

k=0

(b) Continuous if

k=1

k

(d) Continuous if

k=-1