Question

How to solve lim ((x^2 +12)^(1/2) - 4)/(2 - (x^3 - 4)^(1/2)) when x goes to 2 without use L'Hôspital. Thanks!

Answer 1

\[\Large\lim_{x\to2} \frac{\sqrt{x^2 +12} - 4}{2 - \sqrt{x^3 - 4}}\]Just wanted to make that a bit easier to look at.

Answer 2

Why can't you use L'Hôpital's rule?

Answer 3

I tried multiplying by the conjugate but it gets really, really messy.

Answer 4

Ahh I imagine that this could be resolved without L'Hôspital. ^^. My doubt is: I should multiply by the conjugate of the denominator or the numerator? Or both? Rsrs

Answer 5

I have a feeling that L'Hôpital's rule would make this easier. If you're intent on doing without... I'm not sure how you ought to proceed. Generally, multiplying by the conjugate of the denominator is a good method, but when I started down that road you could tell it would get pretty messy.

Answer 6

I saw the conjugate of the numerator. Thanks!