Question

Find $\underset{x\to 1^{+}}{\lim }\left(\frac{1}{x-1}\right).$

Answer 1

$$\begin{gathered} \underset{x\to 1^{+}}{\lim }\left(\frac{1}{x-1}\right) \\ \mathrm{Let}x=1+h,\mathrm{where}h\to 0. \\ \underset{h\to 0}{\lim }\left(\frac{1}{1+h-1}\right) \\ =\infty \end{gathered}$$