Determining Limits: Simplifying Nasty Denominator

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The discussion focuses on finding the limit of the function f(x) = [(1+x)1/2 - 1] / [(1+x)1/3 - 1] as x approaches 0 without using L'Hopital's Rule. The initial approach involved multiplying by the conjugate of the numerator, but this led to a complex denominator that was difficult to simplify. A participant suggested using Taylor series for simplification, which is a valid approach. Ultimately, another user realized that multiplying by an expression to achieve a sum of cubes could help resolve the limit. The thread concludes with the acknowledgment that the problem has been addressed satisfactorily.
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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?
 
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May you use taylor series?
 
mathmadx said:
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

(Thread can be closed now.)
 

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