## anonymous 5 years ago Find the lim x->4 of ((x^1/2)-2)/(x-4)

1. watchmath

Are we allowed to use L'Hospital rule?

2. anonymous

yes.

3. anonymous

i have the answer i just dont know how to get there.

4. watchmath

Then you just need to differentiate the top and the bottom and then compute the limit.

5. anonymous

yeah im completely stuck and dont understand it.

6. watchmath

$$\lim_{x\to 4} \frac{\sqrt{x}-2}{x-4}=\lim_{x\to 4}\frac{\frac{1}{2}x^{-1/2}}{1}=\frac{1}{4}$$

7. anonymous

thanks!

8. anonymous

Can also solve this one with conjugate of (sqrt x) -2 multiply top and bottom by (sqrt x) +2 that will eventually get you ((sqrt x)-2)^2 in the numerator which equals x-4 x-4's cancel giving you 1/(sqrt x) =2 in denominator : substitute limit 1/(2+2) = 1/4

9. watchmath

That's correct! :D