Mohon bantuannya master Matematika

>pembuktian
[tex] \lim_{n \to 0} \frac{ \sqrt{5+3 \sqrt{x} }-\sqrt{5-3 \sqrt{x} } }{ \sqrt{x} } =\frac{ \sqrt{5+3 \sqrt{0} }-\sqrt{5-3 \sqrt{0} } }{ \sqrt{0} }= \frac{ \sqrt{5}- \sqrt{5} }{0}= \frac{0}{0} [/tex]

>penyelesaian
 [tex]\lim_{n \to 0} \frac{ \sqrt{5+3 \sqrt{x} }-\sqrt{5-3 \sqrt{x} } }{ \sqrt{x} } \\ \\ =\lim_{n \to 0} \frac{ \sqrt{5+3 \sqrt{x} }-\sqrt{5-3 \sqrt{x} } }{ \sqrt{x} }X \frac{\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }}{\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }} \\ \\ =\lim_{n \to 0} \frac{(5+3 \sqrt{x}) -(5-3 \sqrt{x}) }{ \sqrt{x}(\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }) } \\ \\ = \lim_{n \to 0} \frac{5+3 \sqrt{x} -5+3 \sqrt{x} }{\sqrt{x}(\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }) } [/tex]

[tex] \\ \\ = \lim_{n \to 0} \frac{6\sqrt{x} }{\sqrt{x}(\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }) } \\ \\ = \lim_{n \to 0} \frac{6}{\sqrt{5+3 \sqrt{x} }+\sqrt{5-3 \sqrt{x} }} \\ \\ = \frac{6}{\sqrt{5+3 \sqrt{0} }+\sqrt{5-3 \sqrt{0} }} \\ \\ =\frac{6}{\sqrt{5+0}+\sqrt{5-0}} \\ \\ =\frac{6}{\sqrt{5}+\sqrt{5}} \\ \\ = \frac{6}{ \sqrt{10} } \\ \\ = \frac{3}{5} \sqrt{10} [/tex]