# Evaluate the Following Limit

• Aug 14th 2009, 02:16 PM
Hamza
Evaluate the Following Limit
Hi guys:

I'm having a devil a time figuring out this problem. I could use any step-by-step help ya'll would be willing to lend:

Evaluate the following limits:

lim x-->14

(sqrt of x+2) - 4 / (x-14)^2

Thanks very much!
• Aug 14th 2009, 02:28 PM
mr fantastic
Quote:

Originally Posted by Hamza
Hi guys:

I'm having a devil a time figuring out this problem. I could use any step-by-step help ya'll would be willing to lend:

Evaluate the following limits:

lim x-->14

(sqrt of x+2) - 4 / (x-14)^2

Thanks very much!

The expression can be re-written as $\displaystyle \frac{x - 14}{(x - 14)^2} \cdot \frac{1}{\sqrt{x + 2} + 4}$ ....
• Aug 14th 2009, 05:29 PM
matheagle
using conjugates on $\displaystyle {\sqrt{x + 2} - 4}$

I get $\displaystyle (\sqrt{x + 2} + 4)(\sqrt{x + 2} - 4)=x+2-16=x-14$

In that case I get

$\displaystyle \lim_{x\to 14}{1\over (x-14)(\sqrt{x + 2} + 4)}$

which doesn't exist because you can get plus or minus infinity depending on how you approach 14.