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!

Printable View

- Aug 14th 2009, 02:16 PMHamzaEvaluate 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 PMmr fantastic
- Aug 14th 2009, 05:29 PMmatheagle
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.