Define the function f(x)= cases x -1 x-1 , & 0< x 4, ; x 1, , & x=1, 1, & x=0

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

Problem

Define the function

f(x)=\begin{cases}\dfrac{\sqrt{x}-1}{x-1}, & 0< x\le 4,\; x\neq 1,\\k, & x=1,\\1, & x=0.\end{cases}

Determine the value of

k

that makes

f

continuous on the closed interval

[0,4]