Limit of a rational function with a square-rooted expression in numerator.

[MurdocJensen]

lim as x -> 0, [(x+4)^1/2-2]/x

That's the limit I want to evaluate. I keep running into problems getting to the real limit (1/4).
You don't have to give me the answer, but let me know if I'm missing something simple. Or you can just give me a hint.

 

[gb7nash]

What have you tried so far?

 

[MurdocJensen]

So far I have tried dividing out by (x+4)^1/2. This still gives me an x in the denominator that yields infinity when x->0.

I have also tried dividing out by x, but this gives me fractions in the numerator that, again, give me infiinity.

 

[gb7nash]

Have you learned l'hopital's rule yet?

 

[MurdocJensen]

Yea, but I was able to get the answer by just rationalizing the numerator. I'm going to try l'Hospital now.

EDIT: I thought we only use l'Hospital's rule for lmits that are 0/0 or inf/inf.

 

[gb7nash]

Both methods should work. l'hopital's rule will probably be easier, but rationalizing the numerator is good practice.

 

[MurdocJensen]

But aren't we using l'Hospital's rule for indeterminate forms?

 

[gb7nash]

But aren't we using l'Hospital's rule for indeterminate forms?

You can use l'hopital's rule for 0/0 or +-inf/inf (which in this case you get 0/0). I was just saying there's more than one way of getting the right answer.

 

[MurdocJensen]

gb7: Yea, I'm an idiot for not noticing that. Thanks for the help!