Question

lim x-->0 for [(√x+4) - 2]/x
its the square root of x+4 not just x

Answer 1

This is an indeterminate form that of 0/0 thus we can apply L'Hospital's Rule to obtain the limit as 1/4.

Answer 2

how?

Answer 3

http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Answer 4

thanks

Answer 5

Let me know if you have any more questions :)

Answer 6

\[\lim_{x\rightarrow 0}\frac{\sqrt{x+4}-2}{x}=\lim_{x\rightarrow 0}\frac{\sqrt{x+4}-2}{x}\cdot\frac{\sqrt{x+4}+2}{\sqrt{x+4}+2}=\]\[=\lim_{x\rightarrow 0}\frac{x+4-4}{x(\sqrt{x+4}+2)}=\lim_{x\rightarrow 0}\frac{1}{\sqrt{x+4}+2}=\frac{1}{4}\]