Question

Write the value of $\underset{x\to 0^{-}}{\lim }\frac{\sin x}{\sqrt{x}}.$

Answer 1

$$\begin{gathered} \underset{x\to 0^{-}}{\lim }\left(\frac{\sin x}{\sqrt{x}}\right) \\ \mathrm{Let}x=0-h \\ \mathrm{If}x\to 0,\mathrm{then}h\to 0. \\ \underset{h\to 0}{\lim }\left(\frac{\sin \left(-h\right)}{\sqrt{-h}}\right) \\ \text{The value does not exist.} \end{gathered}$$