How to Find the Limit of This Function Using Only Algebra?

[racer]

Hello there

Find the lim of this function using Algebra alone and without using
Newton Method or L'Hapital Rule, only Algebraic manipulation is allowed.

I have previously posted this lim but no one did solve it algebriaclly, I solved it using
Algebra and uploaded the solution.

Lim \frac{^3\sqrt{x}- 4}{\sqrt{x}- 8}
X ---> 64

The solution
http://img3.freeimagehosting.net/image.php?ae06b74212.jpg

 

[Diffy]

Thanks for the update, although I must have missed the original post. It is quite obvious to me that you would want to factor using the difference of two squares/cubes rule as you have 4 (a perfect square) and 8 (a perfect cube). The only thing that might make one hesitate is that instead of using x^2 and x^3 for the numerator and denominator respectively they use x^(1/3) and x(1/2).

 

[HallsofIvy]

That's impressive! Of course, using L'Hopital's rule (which, I notice, you are not allowed to do) would make it fairly simple.