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

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

Mathematics
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Are we allowed to use L'Hospital rule?
yes.
i have the answer i just dont know how to get there.

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Then you just need to differentiate the top and the bottom and then compute the limit.
yeah im completely stuck and dont understand it.
$$\lim_{x\to 4} \frac{\sqrt{x}-2}{x-4}=\lim_{x\to 4}\frac{\frac{1}{2}x^{-1/2}}{1}=\frac{1}{4}$$
thanks!
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
That's correct! :D

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