This is calculus I by the way. 1. The problem statement, all variables and given/known data Find the given limit by evaluating the derivative of a suitable function at an appropriate point. lim x->1 (x^5-1)/(x-1) 2. Relevant equations None really but they have hints: Hints were: look at the definition of the derivative, and then also let h=x-1. 3. 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?