Question

Calcule lim┬(h→0)〖(√(h+3)-√3)/h〗

Answer 1

$\lim_{h \to 0} \frac{ \sqrt{h+3}- \sqrt{3} }{h} \\ =\lim_{h \to 0} \frac{ \sqrt{h+3}- \sqrt{3} }{h} \frac{\sqrt{h+3}+ \sqrt{3}}{\sqrt{h+3}+ \sqrt{3}} \\ = \lim_{h \to 0} \frac{h+3-3}{h(\sqrt{h+3}+ \sqrt{3})} \\ = \lim_{h \to 0} \frac{1}{\sqrt{h+3}+ \sqrt{3} } = \frac{1}{2 \sqrt{3} }$