Prove that f(x) = x^(1/3) is continuous at x = c for c>0.

Not sure how to even start... Any help would be appreciated.

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- Oct 2nd 2010, 04:35 PMshannu82Continuity Proof
Prove that f(x) = x^(1/3) is continuous at x = c for c>0.

Not sure how to even start... Any help would be appreciated. - Oct 2nd 2010, 06:05 PMbondesan
shannu82,

A function is continuous at a point $\displaystyle x=c$ if it satisfies two conditions:

1 - $\displaystyle f(c)$ exists, and

2 - $\displaystyle \lim_{x\to c} f(x) = f(c)$.

The proof is just a matter of verifying this conditions. I hope it helps.