- #1

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## Homework Statement

I have the limit: lim [ (x+h)^2/3 - x^(2/3) /h ]

How would I further simplify and evaluate this limit.

**2. The attempt at a solution**

I have tried using a change of variable and using this in the sum of cubes formula (i.e. (x+h)^(2/3) = a, x^(2/3) = b, and then plugging this into the sum of a cube equation. This did not help and just further complicated matters.

Next, I tried multiplying the numerator and denominator by {x+h)^(1/3) + x^(1/3) to cancel out the roots, but this just made new ones that were even harder to factor out.

I keep trying variations of the two methods I just described, but none of them work. Any direction or help on what to do next would be great. Thanks!