- #1
swiftleaf
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This is calculus I by the way.
Find the given limit by evaluating the derivative of a suitable function at an appropriate point.
lim x->1 (x^5-1)/(x-1)
None really but they have hints:
Hints were: look at the definition of the derivative, and then also let h=x-1.
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?
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?