# Limit of a function with a radical in numerator

1. Jan 14, 2014

### Tyrannosaurus_

1. The problem statement, all variables and given/known data

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

3. 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!

Last edited: Jan 14, 2014
2. Jan 14, 2014

### HallsofIvy

Staff Emeritus
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.

3. Jan 14, 2014

### 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.