Final Exam Extended Response Questions NAME: 1. (10 points) Complete (a) through (d) to find a simplified expression for , h # 0 using the function defined below. f(x) = 5x - 9x2 Simplify as much as possible for each step, each of (a) through (d). (a) (1 point) f(a) = (b) (4 points) f(ath) = (c) (4 points) flat h) - f(a) = (d) (1 point) (ath) - f(a) h2. (4 points) Find the partial fraction decomposition for the rational function given below. 3. Find all real solutions of x for the equations below. Be sure to give exact numeric values and show the algebra you use to ensure full credit. r (x) = - x - 3 x3 + 3x (a) (3 points) 2e2x - 5xe2x = 0 Use the first two steps given below in your answer. Step 1: - x - 3 A Bx + C x(x2 + 3) x2 + 3 Step 2: Multiple both sides of the equation by x(x2 + 3) (b) (3 points) In(x + 1) + In(x) = 3