Question

hi, how can i solve lim((sqrt(5+h)-sqrt(5))/h) where h->0

Answer 1

\[lim_{h\rightarrow 0}\frac{\sqrt{5+h}-\sqrt5}{h}\]\[=lim_{h\rightarrow 0}\frac{\sqrt{5+h}-\sqrt5}{h} \times \frac{\sqrt{5+h}+\sqrt5}{\sqrt{5+h}+\sqrt5}\]\[=lim_{h\rightarrow 0}\frac{(\sqrt{5+h}-\sqrt5)(\sqrt{5+h}+\sqrt5)}{h(\sqrt{5+h}+\sqrt5)}\]Can you simplify it?

Answer 2

only i little, \[\lim_{h \rightarrow 0} \frac{ h }{ h \sqrt{5+h} +h \sqrt{5}}\]

Answer 3

Don't need to expand the numerator, since you can cancel a common factor.

Answer 4

yep u right
\[\lim_{h \rightarrow 0} \frac{ 1 }{ \sqrt{5+h} +\sqrt{5} }\]

Answer 5

Now, evaluate the limit.

Answer 6

\[\lim_{h \rightarrow 0} \frac{ 1 }{ 2\sqrt{5} } = \frac{ 1 }{ 2\sqrt{5} }\]

thanks a lot calisto !

Answer 7

Welcome :)

Answer 8

Multiplying a conjugate is the key to solve this question :)

Answer 9

jeah ive got blocked, thinking in silly ways ;)