# Limit

• November 28th 2011, 09:23 PM
asi123
Limit
Hey guys.

Can I please have some help with this limit over here

ImageShack&#174; - Online Photo and Video Hosting

Thanks a lot.
• November 28th 2011, 09:31 PM
asi123
Re: Limit
BTW

I cant use l'Hôpital's rule.

I'm trying to help someone how haven't learned how to Derivative yet.

Thanks a lot.
• November 28th 2011, 09:39 PM
Prove It
Re: Limit
Quote:

Originally Posted by asi123
BTW

I cant use l'Hôpital's rule.

I'm trying to help someone how haven't learned how to Derivative yet.

Thanks a lot.

You should start by rationalising the numerator, then dividing top and bottom by the highest power of x.
• November 28th 2011, 09:56 PM
asi123
Re: Limit
Well, This is what I got.

ImageShack&#174; - Online Photo and Video Hosting

I cant put zero into that, it doesn't give me much, right?

Thanks a lot.
• November 28th 2011, 10:14 PM
princeps
Re: Limit
Quote:

Originally Posted by asi123
Hey guys.

Can I please have some help with this limit over here

ImageShack&#174; - Online Photo and Video Hosting

Thanks a lot.

$\lim_{x \to \0}\frac{\sqrt{x^2+1}-1}{\sqrt{x^2+16}-4} \cdot \frac{(\sqrt{x^2+1}+1)(\sqrt{x^2+16}+4)}{(\sqrt{x^ 2+1}+1)(\sqrt{x^2+16}+4)}=$

$=\lim_{x \to \0}\frac{x^2 \cdot (\sqrt{x^2+16}+4)}{x^2 \cdot (\sqrt{x^2+1}+1)}$
• November 28th 2011, 10:20 PM
asi123
Re: Limit
Thanks a lot.