C) 2 D) 4 E) 6. ? A) 0 B) 1 C) 1 D) The limit does not exist.

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1 . The asymptotes of the graph of the parametric equations = t, y = t t + are A) =, y = B) = only C) =, y = D) = only E) =, y =. What are the coordinates of the inflection point on the graph of y = ( + ) Arctan? A) (,) B) (,) C) (,) D), E), 3. The Mean Value Theorem guarantees the eistence of a special point on the graph of y = etween (,) and (,). What are the coordinates of this point? A) (,) B) (,) C) (, ) D), E) None of the aove 8. + = A) B) 3 C) D) E) 6 5. If 3 + y + y =, then the value of dy at = is A) B) C) D) E) not defined h 8 lim 6. What is h? A) B) C) D) The limit does not eist. h E) It cannot e determined from the information given. 7. For what value of k will + k have a relative maimum at =? A) B) C) D) E) None of these 8. If h() = ƒ () g (), ƒ ' () = g(), and g ' () = ƒ(), then h' () = A) B) C) f()g() D) [ g()] = [f()] E) [ g() + f()] 9. The area of the closed region ounded y the polar graph of r = 3 + cos q is given y the integral / A) 3 + cos q dq B) 3 + cos q dq C) (3 + cos q) dq D) ( 3 + cos q) dq / E) 3 + cos q dq. + = A) B) ln C) D) ln E) +. The point on the curve + y = that is nearest the point, occurs where y is A) B) C) D) E) none of the aove

2 . If F() = e t dt, then F ' () = A) e B) e C) e + + D) e E) e e 3. The region ounded y the ais and the part of the graph of y = cos etween = and = is separated into two regions y the line = k. If the area of the region for k is three times the area of the region for k, then k = A) arc sin B) arc sin 3 C) 6 D) E) 3. If y = + and u =, then dy du = A) + ( ) B) 6 + C) D) E) 5. If ƒ ' () and g ' () eist and ƒ ' () > g ' () for all real, then the graph of y = ƒ() and the graph of y = g() A) intersect eactly once B) intersect no more than once C) do not intersect D) could intersect more than once E) have a common tangent at each point of intersection 6. If y is a function of such that y ' > for all and y " < for all, which of the following could e part of the graph of y = ƒ()? 7. The graph of y = 5 5 has a point of inflection at A) (,) only B) (3,6) only C) (, 56) only D) (,), and (3, 6) E) (,) and (, 56) 8. ƒ() = + 3 for all and the value of the derivative ƒ ' () at = 3 is A) B) C) D) E) noneistent 9. A point moves on the X ais in such a way that its velocity at time t (t > ) is given y v = ln t. At t what value of t does v attain its maimum? A) B) e / C) e D) e 3/ E) There is no maimum value for v.

3 . An equation for a tangent to the graph of y = arc sin at the origin is A) y = B) y = C) = D) y = E) y =. At =, which of the following is true of the function f defined y ƒ() = + e? A) ƒ is increasing B) ƒ is decreasing C) ƒ is discontinuous.d) ƒ has a relative minimum E) ƒ has a relative maimum.. If ƒ() = t 3 dt, which of the following is FALSE? + A) ƒ() = B) ƒ is continuous at for all. C) ƒ() > D) ƒ'() = 3 E) ƒ( ) > 3. If the graph of y = ƒ() contains the point (,), dy =, and ƒ() > for all, then ƒ() = ye A) 3 + e B) 3 + e C) + e D) 3 + e E) 3 + e. If sin = e y, < <, what is dy is terms of? A) tan B) cot C) cot D) tan E) csc 5. A region in the plane is ounded y the graph of y =, the ais, the line = m, and the line = m, m>. The area of this region A) is independent of m B) increases as m increases C) decreases as m increases D) decreases as m increases when m < ; increases as m increases when m > E) increases as m increases when m < ; decreases as m increases when m > 6. + is A) B) C) D) E) none of the aove 7. If dy = tan, then y = A) tan + C B) sec + C C) ln sec + C D) ln cos + C E) sec tan + C lim e 8. What is? tan A) B) C) D) E) The limit does not eist. 9. ( ) 3/ = A) 3 B) C) D) E) 3 3 () n n 3. is the Taylor series aout zero for which of the following functions? n! n A) sin B) cos C) e D) e E) ln ( + ) 3. If ƒ ' () = ƒ() and ƒ() =, then ƒ() = A) e + B) e C) e D) e E) e 3. For what values of does the series n +... converge? A) No values of B) < C) ³ D) > E) All values of

4 33. What is the average (mean) value of 3t 3 t over the interval t? A) B) 7 C) 8 D) 33 E) 6 3. Which of the following is an equation of a curve that intersects at right angles every curve of the family y = + k (where k takes all real values)? A) y = B) y = C) y = 3 3 D) y = 3 3 E) y = ln 35. At t = a particle starts at rest and moves along a line in such a way that at time t tis acceleration is t feet per second per second. Through how many feet does the particle move during the first seconds? A) 3 B) 8 C) 6 D) 96 E) The approimate value of y = + sin at =., otained from the tangent to the graph at =, is A). B).3 C).6 D). E). 37. Of the following choices of d, which is he largest that could e used successfully with an aritrary e in an epsilon delta proof of ( 3 ) = 5? A) = 3e B) = e C) = e lim D) = e E) = e If ƒ() = ( + ) ( 3), then ƒ ' () = A) ln (8e) B) ln (8e) C) 3 ln D) E) If y = tan u, u = v v, and v = ln, what is the value of dy at = e? A) B) e C) D) e E) sec e. If n is a non negative integer, then n = ( ) n for A) no n B) n even, only C) n odd, only D) nonzero n, only E) all n. If ƒ() = 8 3 for ƒ() =, then elsewhere ƒ() is a numer etween A) and 8 B) 8 and 6 C) 6 and D) and 3 E) 3 and. If cos = ƒ() sin, then ƒ() = A) sin + co + C B) sin + C C) cos sin + C D) cos sin + C E) ( ) cos sin + C 3. Which of the following integrals gives the length of the graph of y = tan etween = a and =, where < a < <? A) + tan B) + tan a a C) a + sec D) a + tan E) a + sec. If ƒ " () ƒ ' () ƒ() =, ƒ ' () = e, and ƒ() =, then ƒ() = A) e + e B) C) D) e E) e

5 ( + ) 5. The complete interval of convergence of the series k is k= A) < < B) C) < D) < E) ANSWERS: ) C ) E 3) B ) D 5) E 6) B 7) D 8) C 9) D ) A ) B ) E 3) C ) D 5) B 6) B 7) B 8) E 9) C ) A ) B ) E 3) D ) C 5) A 6) C 7) C 8) D 9) C 3) D 3) C 3) B 33) A 3) D 35) A 36) B 37) D 38) A 39) D ) E ) D ) B 3) E ) E 5) E