Answer:
Solution given:
[tex]Lim_{h\rightarrow} \frac{\sqrt{x+h}-\sqrt{x}}{h}[/tex]
The given expression takes the form of [tex]\frac{0}{0}[/tex]
when h=0
now
[tex]lim_{h\rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h}*\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}[/tex]
[tex]lim_{h\rightarrow 0}\frac{(x+h)-x}{h*({\sqrt{x+h}+\sqrt{x}})}[/tex]
[tex]lim_{h\rightarrow 0}\frac{h}{h*({\sqrt{x+h}+\sqrt{x}})}[/tex]
[tex]lim_{h\rightarrow 0}\frac{1}{({\sqrt{x+h}+\sqrt{x}})}[/tex]
=[tex]\frac{1}{\sqrt{x+0}+\sqrt{x}}[/tex]
=[tex]\frac{1}{2\sqrt{x}}[/tex]
