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Question 9.3
Question 9.3
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TZ
leumasic
Official
3 months ago
We have
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\begin{align*} f'(a)&=\lim_{h\to 0}\frac{f(a+h)-f(a)}{h} \\ &=\lim_{h\to 0}\frac{\sqrt{a+h}-\sqrt{a}}{h} \\ &=\lim_{h\to 0}\frac{a+h-a}{h(\sqrt{a+h}+\sqrt{a})} \\ &=\lim_{h\to 0}\frac{1}{\sqrt{a+h}+\sqrt{a}} \\ &=\frac{1}{2\sqrt{a}}. \end{align*}
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