Fall 2006 Math 151 Common Exam 1B Thu 28 Sep 2006 For official use only Name print QN PTS 1 13 Signature 14 15 Instructor 16 17 18 Section 19 20 Seat Total Instructions 1 In Part 1 Problems 1 13 mark the correct choice on your ScanTron form using a No 2 pencil For your own record also mark your choices on your exam ScanTrons will be collected from all examinees after 90 minutes and will not be returned 2 Be sure to write your name section number and version of the exam 1A or 1B on your ScanTron 3 In Part 2 Problems 14 20 present your solutions in the space provided Show all your work neatly and concisely and indicate your final answer clearly You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Neither calculators nor computers are permitted on this exam 5 Please turn off all cell phones so as not to interrupt other students 1 Part 1 Multiple Choice 52 points Read each question carefully Each problem in Part 1 is worth 4 points 1 The curve given parametrically by the equations x cos t y sin2 t 0 t 2 forms a part of a hyperbola b part of a circle c a line segment d part of a parabola e none of the above x 2 1 x 3 2 Which of the following statements is true about the graph of f x 4 x 2 x 3 a The graph has one vertical asymptote x 2 and no horizontal asymptotes b lim f x lim f x x 2 x 2 c The graph has vertical asymptotes x 2 x 2 x 3 and horizontal asymptote y 1 d The graph has vertical asymptotes x 2 x 2 and horizontal asymptote y 1 e lim f x does not exist x 3 3 Evaluate lim x x 2 4x 4x 1 1 4 b 1 c 4 d 0 a e 1 2 4 One of the following intervals contains a number c such that c3 2c 12 Which one a 4 b 3 4 c 0 1 d 1 2 e 2 3 5 Refer to the graph of y f x given below then decide which of the following statements is false 3 2 y 1 2 1 0 1 x 2 3 1 a lim f x 2 x 2 b lim f x 2 x 1 c lim f x 0 d lim f x 1 x 0 x 1 e lim f x 2 x 1 6 The following statements pertain to the figure below Which statements are true i a b c ii a b c iii b a c a Only statement ii is true b Only statement iii is true c Statements ii and iii are both true d Only statement i is true e Statements iii and iv are both true c b a 7 If a h1 4i and b h2 3i find 3a 2b a h 4 17i b h3 1i c h5 6i d h 1 18i e h7 6i 3 iv b c a 9 h 3 8 Evaluate lim h 0 h a does not exist b c 0 d 1 1 e 6 9 Suppose v and w are vectors with v 2 and w 3 If the angle between v and w is 60 degrees compute v 2w 3v a 12 3 2 b 6 3 12 c 0 d 6 e 2 13 10 Suppose f is a function defined on an open interval containing the point 3 and that f 3 2 Which of the following statements is always true a If lim f x 2 then f is differentiable at x 3 x 3 b If lim f x 2 then f is continuous at x 3 x 3 c If lim f x exists then f is continuous at x 3 x 3 d Either lim f x or lim f x must exist x 3 x 3 e lim f x 2 x 3 4 11 Let a 2i 3j and b i 2j Find compa b the scalar projection of b onto a a b c d e 4 13 13 4 5 5 4 4 13 13 4 5 5 12 Find lim x 2 3x 6 6 3x a does not exist b 1 c 1 d 0 e 1 x 2 3 if x 0 2x 3 if x 0 13 Let f be the function defined by f x 1 if x 0 x 1 Which of the following statements is true a f is continuous everywhere b f is not continuous at x 1 c f is not continuous at x 0 because lim f x does not exist x 0 d f is not continuous at x 0 because lim f x does not equal f 0 x 0 e All of the above statements are false 5 Part 2 Work Out Problems 48 points Partial credit is possible SHOW ALL STEPS 14 Differentiate you need not simplify 2 3 2 x x a 3 points y 4 b 3 points f x 3x c 3 points g s d 3 points h t t 3 2t 5 7t 6 t 7 t 5 t 3 t 4 2x 5 7s 3 8s 2 15 A particle is moving in the x y plane Its position at time t is given by the position vector 2 3 r t 4t i t 9t 2 j Distances are in feet times are in seconds a 2 points At what point is the particle at time t 2 Write your answer in the form a b b 3 points What is the particle s velocity at time t 2 c 2 points What is the particle s speed at time t 2 You need not simplify d 2 points At what time s will the particle s velocity be vertical parallel to j 6 16 a 3 points Find parametric equations for the line that contains the points 4 9 and 6 2 b 2 points The graph of 3x 2y 5 is a line L Which of the following statements is true Circle the true statement i The vector 2i 3j is parallel to the line L ii The vector 2i 3j is perpendicular to the line L iii The vector 2i 3j has no special relationship with L c 2 points Find a unit vector that is orthogonal to the vector 2i 5j 17 Find the following limits a 3 points b 3 points lim x2 4 x2 x 6 lim 1 2x 3x 2 1 x x2 x 2 x 7 18 5 points Find an equation of the tangent line to the graph of f x x2 Write your answer in the form Ax By C where A B C are integers 2x 7 at the point where x 1 6x 4 2 f x 25 19 4 points Suppose f is a function such that …
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