#1,#2

Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work. Problem 2. For every real number a * 0, for every nonnegative integer n, for the function f(x) = x", simplify the limit, lim f(q . a) - f(a) (q . a) - a Evaluate your simplified limit using the formula for a finite geometric sum, 1 + q+ q' +.. . + qn-1 q" - 1 q-1 Use this to compute f'(a) for a + 0