Limit of a function with a radical in numerator

[Tyrannosaurus_]

Homework Statement

Evaluate the limit as x → 0 (zero), if it exists, for:
[(x+4)^(1/2) - 2]/x

The Attempt at a Solution

I was not too sure at an elegant solution because nothing like this existed in the coursework. The best I could think of was to evaluate the limit on each side of zero.

I tried: evaluate x → 0⁺ (I used 0.000001)., then I tried: evaluated x → 0^- (I used -0.000001). Both of these values are very close to 0.25.

How can I solve this problem with a little more elegance? Many thanks to the repliers!

 

[HallsofIvy]

That function, \dfrac{\sqrt{x+ 4}- 2}{2}, is made entirely of continuous functions so is continuous itself. The limit "as x goes to 0" is simply the value at x= 0.

 

[LCKurtz]

I don't know if the OP had a typo and fixed it or whether Halls miscopied it but given the expression is$$
\frac{\sqrt{x+ 4}- 2}{x}$$try rationalizing the numerator.