1. [20 pts] Directions: Fill in the circle next to the correct response(s). Q1: Multiselect [3 pts] Suppose f(x) is an infinitely differentiable function for which f(3)(0) = -24. Of the polynomials listed below, select ALL which could be a Taylor polynomial centered at x = 0 for f(x)? A PA(2) = 2+ 4x2 - 823 - 2424 B p3(x) = x2 - 423 Cp3(a) = 1+x+4x2+4x3 D PA(2) = 4-3x + 823 - 4x4 E PA(x) = 3x - 6x2 - 4x3 F P3(x) = 1-22 -623 Q2: Multiple Choice [3 pts] Fill in the circle next to the best response. 72k+1 If f (ac) = (2k + 1) . k! . use the Taylor series for f to determine lim f(x) - x x-+0 3x3 + 4x6 A o B 1 C 12 E The limit does not exist F None of these Q3: Multiple Choice [3 pts] Fill in the circle next to the best response. 4k Suppose that f(x) = 9/2 + 3 ck. Determine f'(0). A BO C D D f'(0) does not exist E) None of theseQ4: Multiple Choice [3 pts] Fill in the circle next to the best response. The third degree Taylor polynomial centered at x = 0 for f(x) = xe2 is: A x + 2x + 4x3 Bx+ 2x2+23 Cx -273 D x + 2x2+ 2x3 (E) 1 + 2x + 2x2+ F None of these