# Math Help - Limits

1. ## Limits

$\lim_{x \to 14}\frac{\sqrt{x+2}-4}{70-19x+x^2}$

$\lim_{x \to 13}\frac{-26+2x}{\sqrt{x+3}-4}$

2. ## Re: Limits

Originally Posted by Lotte1990

$\lim_{x \to 14}\frac{\sqrt{x+2}-4}{70-19x+x^2}$

$\lim_{x \to 13}\frac{-26+2x}{\sqrt{x+3}-4}$
$L_1=\displaystyle \lim_{x \to 14}\frac {(x-14)}{(x-14)(x-5)(\sqrt{x+2}+4)}=\frac{1}{72}$

$L_2=2\cdot \displaystyle \lim_{x \to 13} \frac{(x-13)(\sqrt{x+3}+4)}{(x-13)}=16$

4. ## Re: Limits

For the first one, rationalise the numerator by multiplying top and bottom by the top's conjugate.
For the second one, rationalise the denominator by multiplying top and bottom by the bottom's conjugate.

5. ## Re: Limits

A useful fact for problems of this sort: if P is a polynomial such that P(a)= 0 then x- a is a factor or P(x).

Also, if you have a term involving a root that is 0 when x= a, then rationalizing it will give a polynomial with a factor of x- a.