- #1

swiftleaf

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## Homework Statement

Find the given limit by evaluating the derivative of a suitable function at an appropriate point.

lim x->1 (x^5-1)/(x-1)

## Homework Equations

None really but they have hints:

Hints were: look at the definition of the derivative, and then also let h=x-1.

## The Attempt at a Solution

I can solve this question two ways (L'hospital and regular factoring)

Factor (x^5-1), to get (x-1)(x^4+x^3+x^2+x+1).

The (x-1)'s cancel out and you are left with:

lim x->1 (x^4+x^3+x^2+x+1) = 5

Or L'hospital 5x^4 = 5

I really don't understand what method the question is asking me to do. I can try the definition of a derivative method but I get really stuck..

[f(x+h)-f(x)]/h

(assuming my function is (x^5-1)/(x-1))

[(x+h)^5-1]/(x+h)-(x^5-1)/(x-1)) / h

Then that just looks like a mess when I expand it.. I doubt this is the way they want us to do it.. anyone want to provide any insight on how to do this?