Determining Limits: Simplifying Nasty Denominator

[SpringPhysics]

Homework Statement

Determine the limit as x approaches 0 of

f(x) = [(1+x)^1/2 - 1] / [(1+x)^1/3 - 1]

Homework Equations

I am not allowed to use L'Hopital's Rule.

The Attempt at a Solution

I multiplied by the conjugate of the numerator and got a nasty denominator that I cannot simplify nicely. Can someone give me a lead?

 

[mathmadx]

May you use taylor series?

 

[SpringPhysics]

May you use taylor series?

I just found out that I should multiply by an expression to get a sum of cubes (totally forgot about that). =P

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