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

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Homework Help Overview

The discussion revolves around evaluating a limit without using l'Hôpital's rule, specifically focusing on a limit problem presented by the original poster. The problem involves square roots in the numerator and denominator.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss multiplying the numerator and denominator by specific expressions to simplify the limit. There is a question regarding how this approach affects the signs and terms involved.

Discussion Status

Some participants have provided guidance on a potential method for simplification, while others are questioning the implications of the suggested approach. The discussion reflects a mix of exploration and clarification without reaching a definitive conclusion.

Contextual Notes

The original poster has indicated a constraint of not using l'Hôpital's rule and is assisting someone who has not yet learned about derivatives.

asi123
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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

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

ehild
 


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.
 


Ops, that's the solution.

Thanks a lot.
 


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

ehild
 

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