How can I solve this limit without using l'Hôpital's rule?

[asi123]

Homework Statement

Hey guys.

Can I please have some help with this limit over here

http://imageshack.us/photo/my-images/839/targil.jpg/

BTW

I can't use l'Hôpital's rule.

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

Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[ehild]

Multiply both the numerator and denominator with
$$(\sqrt{x^2+1}+1)(\sqrt{x^2+16}+4)$$ and simplify.

ehild

 

[asi123]

It will switch between the numerator and the denominator and will change the sign of the 1 and 4.

How can that help?

Thanks a lot.

 

[asi123]

Ops, that's the solution.

Thanks a lot.

 

[ehild]

You are welcome. And remember the method, it is always useful when you have difference including square root(s)

ehild