Question

Find the lim x->4 of ((x^1/2)-2)/(x-4)

Answer 1

Are we allowed to use L'Hospital rule?

Answer 2

yes.

Answer 3

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

Answer 4

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

Answer 5

yeah im completely stuck and dont understand it.

Answer 6

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

Answer 7

thanks!

Answer 8

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

Answer 9

That's correct! :D