Limit of (1/√x - 1/2)/(x - 4) as x approaches 4

[RadiationX]

For the life of me I can't figure this limit out

lim ( 1/sqt x - 1/2)/ ( X -4)
x->4


I KNOW THE ANSWER IS -1/16 BUT WHAT ARE THE STEPS NECESSARY TO REACH THIS SOLUTION?
THANKS FOR ANY HELP.

 

[Tide]

Try l'Hopital's rule- it works!

 

[maverick280857]

Another way (if I understand your problem correctly) would be to rewrite the given function as

$$\frac{\frac{1}{\sqrt{x}} - \frac{1}{2}}{(\sqrt{x}-2)(\sqrt{x}+2)}$$

if you're not familiar with L-Hospital's Theorem.

Cheers
Vivek