SAMPLE EXAM I Section I Part A Directions: Solve each of the following problems, using available space for scratchwork. After examining the form of the choices, decide which is the best of the choices given. Do not spend too much time on any one problem. Calculators may NOT be used on this part of the exam. In this test: Unless otherwise specified, the domain of a function / is assumed to be the set of all real numbers i for which f(x) is a real number. 1. If /(i) = z2 — 9 is continuous at x = —3, then /(—3) = 1 +3 (A) 3 (B)-3 (C) 0 (D) 6 (E) -6 Answer 2. If x > 0, 13 Answer SAMPLE EXAM I 3. If /(z) = «"'"*, how many zeros does /'(x) have on the closed interval [0,2ir] ? (A)l (B)2 (C)3 (D)4 6. (E)5 If /(x) = , then /'(O) = (A) -2 (B) 0 WT Answer (E) 1 Answer 4. I lira 108x$ + 106x< + 104zJ "~ 10»x« + 10rx« + 105x3 (A) 0 (B) 1 (D) — ( ' 10 The equation of the tangent line to the curve x 2 + y 2 = 169 at the point (5, -12) is (A)5y-12x = -120 (B)5x-12y = 119 (C) 5x - 12j = 169 Answer (D) 12x + 5y = 0 (E) 12x + 5y = 169 5. The graph of which function has y = -1 as an asymptote ? —x 1-x Answer ( C ) y = ln(x X •x + 1 (E) y =- 1-x S. If /(x) = x - 1 and j(x) = x2 + 1, then !(g(x)) = g(f(x)} (A)-A Answer when x = (E)0 Answer SAMPLE EXAM I 11. If the graph of f ( x ) = 2z2 + - has a point of inflection at x = -1, then the value of k is (C)2 (D)-2 (E)0 Answer 9. 12. For the figure above, the area of the shaded region is The graph of y = \/z2 + 1 is symmetric with respect to which of the following ? I. The i-axis II. The y-axis III. The origin (A) I only (C)f (B) II only (D)f (C) III only (D) II and III only (E)f (E) I, II, and III Answer Answer 10. 13. / sin(3;x + 4) dx •. (A) Arcsin | + C (A) -icos(3x + 4) + <7 O (B) 2^4 - i2 + C (B) - cos(3z + 4) + C (C) Arcsinz + C (C) -3cos(3i + 4) + C (D) VJ^+C (D) cos(3i + 4) + C (E) i cos(3i + 4) + C (E)iArcsinf + C Answer SAMPLE EXAM I 9 Answer SAMPLE EXAM I 14. («""*) 17. ,3 In (C)x 3 (B)- (D) 3x' (E)3 Suppdse f(x) = In3x and /"'(*) denotes the inverse of /. Th«n / /"*(*) dx (A) 3e' Answer Answer n 15. For what values of x is the graph of y = —— concave downward ? 18. If y = x(*3) for x > 0, then ~ = ax (A) No values of x (B) z < 4 (B) 4x3 (C) i > -4 (E)3x<*' +s >lnx (D) * < -4 Answer (IE) i > 4 Answer 19. 16. A particle moves along the i-axis in such a way that its position at time t is given by x(t) = . What is the acceleration of the particle at time t = 0 ? A particle..moves on the z-axis so that at any time t its velocity v(t) = sin 2t subject to the condition i(0) = 0 where x(t) is the position function. Which of the following is an expression for x(t) ? (A) cos 2* + i w-S (B)-|sm2t+i (B)-4 (C)-|cos2t (C) 4 (D) -icos2J+i (D) 2 (E)-icos2<-| (E) -2 Answer Answer 20. If, for all values of *, /(x) < 0 and /"(x) > 0, which of the following curves could be part of the graph of / ? (A) „ (B) (C) „ y3 x , 23. Jo x + 1 (A)21n2 „ (B)61n2 ( V , "J> 1 ,. , \\ (C)3-21n2 (D)3 + 21n2 (E)3 + ln3 Answer , (D) •"' f (E) ,/ *x \ The maximum value of /(x) = 2x3 - 9x2 + 12x - 1 on [-1,2] is 24. (A)0 Answer (C) 2 21. If /r x sec2 x dx = f ( x ) + In | cos z| + C, then /(x) '= (D) 3 (E)4 (A) tan* (B) |x2 (C)xtanx (D)x2tanx (E)tan 2 x Answer Answer ' . t 25. 22. If / (x2 - 2x + 2) dx is approximated by three inscribed rectaagles of equal width on the ./o x-axis, then the approximation is (A) 24 (B)26 (C)28 (0)48 Let /(x) be the function denned by /(x) = I *' x - ° [ x + 1, x > 0 /•i The value of / xf(x) dx = (E) 76 (E)3 Answer Answer SAMPLE EXAM I 8 • . fl SAMPLE EXAM I

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