Multiple Choice Questions

Let a > 1 be a constant. If f'(x) = 3ar(ax2 +a?)1/2 and f(1) =(a+?)3/2, then f(0) equals (A) -a (B) a (C) a (D) -(a?) (E) None of (A) - (D) The smallest possible slope for a tangent line to the curve y = - 3r + 5x is (A) 6 (B) 2 (C) -2 (D) 4 (E) 14 (F) None of (A) - (E) If f(x) = 4(3*) and n > 2 is an integer, then f(")(1) equals (A) [12 In(3)]" (B) 12(3") (C) 4n3" (D) 12[ In(3)]" (E) None of (A) - (D) Let A, m > 2 be constants. A box with no top is constructed with A metres of material. The length of the box is m times the width of the box. If the volume of the box is maximum, what fraction of A is the area of the base of the box ? (A) A/3 (B) 3/8 (C) (24)/5 (D) 7/16 (E) 1/3 (F) None of (A) - (E) An interest rate of 6% APR, compounded monthly, is assumed. What is (rounded down to the nearest dollar) the present value of a generalized ordinary annuity of $500 paid at the end of each month for one year and then $350 paid at the end of each month for three years after that ? (A) 20, 784 (B) 21, 738 (C) 20, 216 (D) 21, 124 (E) 19,985 (F) None of (A) - (E) The value of lim 27 27%2 is IME n (A) None of (B) - (F) (B) 20/3 (C) 55/3 (D) 18 (E) 64/3 (F) 57/2