Question

$\underset{h\to 0}{lim}\left(\frac{\sqrt{x+h}-\sqrt{x}}{h}\right)$

Answer 1

${lim}_{h\to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}=\frac{0}{0}$

${lim}_{h\to 0}\frac{\frac{1}{2\sqrt{x+h}}-\frac{1}{2\sqrt{x}}}{1}$

$=\frac{1}{2\sqrt{x}}-\frac{1}{2\sqrt{x}}=0$