다음 극한값을 계산하라.
$$\lim_{x\to1}\frac{\sqrt{x}+x-2}{x-1}$$
풀이
\(\displaystyle\lim_{x\to1}\frac{\sqrt{x}+x-2}{x-1}=\lim_{x\to1}\frac{(\sqrt{x}+2)(\sqrt{x}-1)}{(\sqrt{x}+1)(\sqrt{x}-1)}\)
\(\displaystyle=\lim_{x\to1}\frac{\sqrt{x}+2}{\sqrt{x}+1}=\frac{\sqrt{1}+2}{\sqrt{1}+1}=\frac{3}{2}\)