Mathematics

Mathematics

Problem

Define the function f(x)={x−1x−1,0<x≤4,  x≠1,k,x=1,1,x=0.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 kk that makes ff continuous on the closed interval [0,4][0,4].

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