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## Homework Statement

the limit x->a of [(x+2)^5/3 - (a+2)^5/3] / (x-a)

## Homework Equations

limit laws

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In summary, the limit x->a of [(x+2)^5/3 - (a+2)^5/3] / (x-a) is homework equation. The Attempt at a Solution mentions that differentiation is the shortest way. The restriction is due to the question is apparently brought up before any derivatives are introduced. So apparently this is do-able without using straight up differentiation. The 1/3 is killing me. and i have no idea how to approach it.

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the limit x->a of [(x+2)^5/3 - (a+2)^5/3] / (x-a)

limit laws

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- #2

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Does the formula in the third attempt remind you on something?

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It's done by the chain rule and ##x^\alpha = \exp(\alpha \ln x)##. Perhaps this might help and you may use properties of the exponential function. Another substitution ##y=x+2## should decrease writing work.

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this seems to take care of it - provided you know how to expand a sum of powers to a high level - had to look it up to be honest:

so revised sheet:

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Correct result.fishspawned said:

this seems to take care of it - provided you know how to expand a sum of powers to a high level - had to look it up to be honest:

so revised sheet:

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