MATH 151, FALL 2017 COMMON EXAM I - VERSION A

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1 MATH 11, FALL 017 COMMON EXAM I - VERSION A LAST NAME(print): FIRST NAME(print): INSTRUCTOR: SECTION NUMBER: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited.. TURN OFF cell phones and put them away. If a cell phone is seen during the exam, your exam will be collected and you will receive a zero. 3. In Part 1 (Problems 1-0), mark the correct choice on your ScanTron using a No. pencil. The scantrons will not be returned, therefore for your own records, also record your choices on your exam!. In Part (Problems 1-), present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your final answer. You will be graded not merely on the final answer, but also on the quality and correctness of the work leading up to it.. Be sure to write your name, section number and version letter of the exam on the ScanTron form. THE AGGIE HONOR CODE An Aggie does not lie, cheat, or steal, or tolerate those who do. Signature: 1

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3 Part 1: Multiple Choice (3. points each) 1. Find the cosine of the angle between the vectors 1, and 3,. (a) 13 (b) (c) 13 (d) (e) Find parametric equations of the line that passes through the point (3, 7) and is perpendicular to the vector, 1. (a) x = 3 t, y = 7+t (b) x = 3 t, y = 7 t (c) x = 3 t, y = 7+t (d) x = 3+t, y = 7+t (e) x = +3t, y = 1 7t 3. lim x (a) (b) (c) (d) 0 (e) x +1 x+7 1+e 3x. Calculate lim x +3e 3x. (a) 3 (b) 0 (c) (d) (e) 1 3

4 . Find a vector of length 3 in the same direction as the vector from the point (,3) to the point (1,7). (a) 3 1, (b) (c) (d) 1, , , (e) 3,1 6. Find a Cartesian equation of the curve defined parametrically be x = cost + 3, y = sint + and describe the direction in which the curve is traced out as t increases. (a) (x 3) +(y ) = 1; Clockwise (b) (x 3) +(y ) = 1; Counterclockwise (c) x 9 + y = 1; Clockwise (d) x 9 + y = 1; Counterclockwise (e) None of these 7. For what values of x is f(x) NOT continuous? e x, x 0 f(x) = x +1, 0 < x 3x+1, x > (a) x = 0 only (b) x = 0 and x = (c) x = only (d) x = 0,x = 1, and x = (e) f is continuous everywhere 8. Simplify tan(arccos x) to an algebraic expression. (a) (b) 1 x x x 1 x (c) 1 x x (d) 1+x (e) 1 1+x

5 9. Given the vectors a = 3, and b =,1, find the vector projection of b onto a. 1 (a), (b) (c) 1 13, , 8 (d), 1 (e), Which of the following statements is true regarding the equation x 3 x =? (a) A solution to the equation exists on the interval (1, ) by the Intermediate Value Theorem. (b) A solution to the equation exists on the interval (,3) by the Squeeze Theorem. (c) A solution to the equation exists on the interval (, 3) by the Intermediate Value Theorem. (d) A solution to the equation exists on the interval (1,) by the Squeeze Theorem. (e) None of these statements are true. 11. A force F = 3, is used to move an object from the point (0,) to the point ( 3,3). How much work is done by the force if distance is measured in meters and force is measured in Newtons? (a) 13 J (b) 9 J (c) 10 J (d) 3 J (e) J

6 1. Determine the vertical asymptotes of the function f(x) = (x+3)(x ) x +x 3. (a) x = 1 and x = 3 (b) x = 1 and x = (c) x = 3 only (d) x = only (e) x = 1 only x Calculate lim x 1 x+3 (a) (b) 1 (c) (d) 8 (e) The limit does not exist. 1. Two forces F 1 = 3, and F = 1,3 act on an object. Find the angle that the resultant force makes with the positive x-axis. (a) arctan ( ) 7 (b) arctan ( ) 7 (c) arctan ( ) 7 (d) arctan ( ) 1 (e) arctan ( ) 7 6

7 ( x 3 ) 1. Calculate lim arctan +1 x x x (a) π (b) (c) π (d) 0 (e) 16. What is the average velocity of a particle with position function f(t) = t+3 from t = 1 to t =? (a) 1 (b) 1 3 (c) 3 (d) 9 (e) What is the slope of the line defined by the vector function r(t) = t, 7+3t? (a) 3 (b) 7 (c) 3 (d) 7 (e) 3 7

8 18. Calculate lim x 8 x x. (a) (b) 8 (c) 8 (d) (e) x 19. Calculate lim x 3 x +x 1 (a) (b) 0 (c) 1 (d) 1 7 (e) 0. Consider the graph of f(x) to the right. Which of the following is the graph of f (x)? (a) (b) (c) (d) (e) 8

9 Part : Work Out Directions: Present your solutions in the space provided. Show all your work neatly and concisely and box your final answer. You will be graded not merely on the final answer, but also on the quality and correctness of the work leading up to it. 1. (8 points) Calculate the following limits. [You may not use L Hospital s Rule if you know it.] 1 (a) lim 1 x x x [ (b) lim ln(x+7) ln(x +) ] x 9

10 . (8 points) Use the definition of the derivative to find f (x) for the function f(x) = x x. No points will be given for any shortcut formulas used. 3. (6 points) A plane heads in a direction 10 from the positive x-axis with a speed of 00 mph. The wind is blowing due south (70 from the positive x-axis) at a speed of 30 mph. Find the true (resultant) velocity vector of the plane. 10

11 . (8 points) Consider the function f(x) = ax +7, x <, x = x+a, x > (a) Determine the value of a so that lim x f(x) exists. (b) Is f(x) continuous at x =? Explain mathematically why or why not. FOR INSTRUCTOR USE ONLY Question Points Awarded Points TOTAL