Fall 2007 Math 151 Common Exam 1A Thu 27 Sep 2007 Name print For official use only QN PTS Signature 1 12 13 Instructor 14 15 16 Section 17 Total Seat Instructions 1 In Part 1 Problems 1 12 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 13 17 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 48 points Read each question carefully Each problem in Part 1 is worth 4 points 1 If a rock is thrown upward on the planet Mars with a velocity of 10 m s its height in meters t seconds later is given by y 10t 2t 2 Find its average velocity in m s over the time interval 1 0 1 1 a 8 00 b 5 80 c 7 56 d 6 00 e 4 00 2 Find proja b the vector projection of b h 4 1i onto a h1 2i a h 3 3i 8 2 b 17 17 c h 5 1i 2 4 d 5 5 e h5 1i 9x 6 x 3 Determine the limit lim x x 3 1 a 3 b 9 c 3 d e 9 2 4 Find all vertical asymptotes to the graph of y x 2 2x x2 x 2 a x 1 and x 2 b x 1 only c x 1 only d x 2 and x 1 e There are none 4 x 5 Compute the limit lim x 16 16x x 2 a 1 4 1 128 1 c 32 1 d 8 1 e 16 b 6 A particle s motion in the x y plane is given by x 2 sin t y 4 cos t 0 t 2 Describe its motion as t increases a parabola traversed left to right b ellipse traversed clockwise c circle traversed counterclockwise d ellipse traversed counterclockwise e circle traversed clockwise 3 7 Let a 5i 12j and b 3i 6j Find the magnitude of the vector a b a 328 b 2 c 40 d 10 e 57 8 Find a unit vector that is parallel to the tangent line to the parabola y x 2 at the point 2 4 a 1 5 i 2 5 j b j c 2 5 i 45 j d i e 1 17 i 4 17 j 9 A tow truck drags a stalled car along a road The chain makes an angle of 30 with the road and the tension in the chain is 1500 newtons How much work in joules is done by the truck in pulling the car 1000 meters a 750 000 3 b 1 500 000 2 c 750 000 d 750 000 2 e 1 500 000 4 10 Find the limit lim x 0 5 2x 1 2x 3 x 2 a 0 b 1 c 4 d e 11 In which interval does the equation x cos x 3 have a solution a 0 b 2 c 2 3 d 0 e 2 12 Find an equation of the tangent line to the curve f x 4x 2 x 3 at x 3 Write your answer in slope intercept form a y 3x 18 b y 8x 3x 2 c y 3x 6 d y 4x 2 x 3 x 3 e y 3x 5 Part 2 Work Out Problems 52 points Partial credit is possible SHOW ALL STEPS 13 Differentiate each of the following functions You do NOT need to simplify a 5 points g t 2t 3 4t 3 4 8t 7 t 4 t 1 3 45 b 5 points q x 5x 1 4x 2 8x 3 14 The piecewise function f is defined as follows if x 2 2 x 2 f x x 3 2 1 if 2 x 4 2x 4 if x 4 a 5 points Where is f discontinuous Justify your answer b 5 points Is f differentiable at x 2 If so give the value of f 0 2 and write down the details of its computation If not explain why the derivative does not exist at x 2 In either case justify your answer 6 1 2x Compute f 0 a via the definition of derivative 15 10 points Let f x 16 10 points Compute the derivative of g x x 2 4 and state the domain of the derivative 7 17 12 points Let g x x 2 The graph of f x appears below Graph of f 4 3 y 2 1 0 1 2 1 0 1 2 x 3 4 5 6 Give the values of the following limits or explain why they do not exist a lim f x x 2 b lim g f x x 2 c lim f g x x 2 8
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