Problem: Calculate limit
Problem
Show that
\[\lim_{h→0} \frac{\sqrt{x+h}-\sqrt{x}}{h}= \frac{1}{2\sqrt{x}}\]
Hint:
\[ \frac{\sqrt{x+h}-\sqrt{x}}{h}â‹… \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\]
Solution
Problem
Show that
\[\lim_{h→0} \frac{\sqrt{x+h}-\sqrt{x}}{h}= \frac{1}{2\sqrt{x}}\]
Hint:
\[ \frac{\sqrt{x+h}-\sqrt{x}}{h}â‹… \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\]
Solution