If f(x)=x+k−2x−1f(x) = \frac{\sqrt{x+k} - 2}{x-1}f(x)=x−1x+k−2 has a finite limit as x→1x \to 1x→1, find kkk.
k=3k = 3k=3
k=1k = 1k=1
k=0k = 0k=0
k=−1k = -1k=−1