Fall 2003 Math 151 COMMON EXAM II Test Form A PRINT Last Name First Name Signature ID Instructor s Name Instructor use only Section Multiple choice Q12 Q13 Q14 Q15 Q16 Q17 Q18 Total INSTRUCTIONS 1 In Part 1 Problems 1 11 mark the correct choice on your ScanTron form using a 2 pencil For your own records also record your choices on your exam The ScanTrons will be collected after 1 hour they will NOT be returned 2 In Part 2 Problems 12 18 write all solutions in the space provided All work to be graded must be shown in the space provided CLEARLY INDICATE YOUR FINAL ANSWERS 1 PART 1 MULTIPLE CHOICE PROBLEMS Each problem is worth 4 points NO partial credit will be given Calculators may NOT be used on this part ScanTron forms will be collected after 1 hour 1 If p x x3 12x1 2 9 then p0 4 a 25 b 45 c 49 d 50 e 54 2 Let f x g x and suppose g 2 6 g0 2 1 h 2 3 h0 2 4 Then f 0 2 h x a 3 1 b 4 1 c 4 d 7 3 e 3 3 Let f be the function defined by f x graph of f x 1 x 3 Find the vertical and horizontal asymptotes of the x2 1 a vertical asymptote x 1 horizontal asymptote y 1 b vertical asymptotes x 1 x 1 horizontal asymptote y 1 c vertical asymptotes x 1 x 1 horizontal asymptote y 0 d vertical asymptote x 1 horizontal asymptote y 0 e vertical asymptotes x 1 x 1 horizontal asymptotes y 1 y 3 4 A moving object s position at time t is given by the vector function r t t2 t ii 4 3t 4t2 jj Find the instantaneous velocity of the object when t 2 a 3ii 13jj b 2ii 14jj c 4ii 14jj d 13ii 57jj e none of these 2 5 A line L is the graph of the vector function r t h2 6t 3 4ti The slope of L is a 6 b 4 c 3 2 2 e 3 3 2 d 6 The constant force F 2ii 3jj moves an object along the straight line from the point 1 5 to the point 4 9 Find the work done if distance is in meters force in Newtons a 3 N m b 41 2ii 3jj N m c 41 N m d 2 N m e 2 2ii 3jj N m t4 7 The displacement of a particle moving in a straight line is given by s 6 8t2 where t is time in 4 seconds and distance is in meters What is the average velocity of the particle over the time interval 0 2 a 24 m s b 14 m s c 0 m s d 14 m s e 24 m s 8 Which of the following is true about lim x 3 x 3 x2 9 a The limit does not exist b The limit is 1 c The limit is 6 1 d The limit is 6 e The limit is 0 9 The domain of the function f defined by f x x2 6x is a all real numbers b all numbers except 0 and 6 c x x 6 d x 0 x 6 e x x 0 or x 6 3 10 Evaluate lim x 4 x 4 x2 x 12 a 0 1 b 7 1 c 3 d 1 e 11 Which of the following is a unit vector orthogonal to h3 4i a h 4 3i b h4 3i c 8ii 6jj d 8ii 6jj e none of these 4 PART 2 WORK OUT PROBLEMS Each problem is worth 8 points partial credit is possible Calculators may NOT be used on this part SHOW ALL WORK 12 a 3 points Write the definition of the derivative of a function f at a number c b 5 points Use the definition of the derivative to calculate the derivative of f x 13 a 4 points Find the scalar projection of 4ii 2jj onto i 3jj b 4 points Find the vector projection of 4ii 2jj onto i 3jj 5 2 x at x 1 14 Find an equation for the tangent line to the curve y 2x3 5x2 6 at the point where x 1 15 a 4 points Differentiate f x 3x 6 2x2 4x b 4 points Differentiate g x 4 6x 7x2 2x x3 x4 16 Evaluate lim x2 3x x x 6 17 Find the value of the constant c that makes the function f x x2 1 if x 3 continuous on 2cx if x 3 Clearly EXPLAIN your answer 18 Good writing is expected in this problem a 4 points State the Intermediate Value Theorem b 4 points Use the Intermediate Value Theorem to explain why the equation x3 x 1 0 has a root between 1 and 2 7
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