TAMU Spring 019 Math 151, Spring 019 Common Eam 1 Version A LAST NAME (print): FIRST NAME (print): INSTRUCTOR: SECTION NUMBER: STUDENT ID NUMBER: Directions: 1. No calculators, cell phones, or other electronic devices may be used, and they must all be put away out of sight.. TURN OFF cell phones and put them away. If a cell phone is seen during the eam, your eam 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 eam! 4. In Part (Problems 1 4), 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. 5. Be sure to write your name, section number, and version letter of the eam on the ScanTron form. THE AGGIE CODE OF HONOR On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Page 1 of 11
Part 1: Multiple Choice (3 points each) 1. Find a vector of length 6 that is perpendicular to the vector from point P (, 1) to the point Q(1, 3). 18 1 (a), 13 13 (b) (c) (d) (e) 1 18, 13 13 18, 1 13 13 1, 18 5 5 18, 1 5 5. A woman walks due east on the deck of a ship at 3 mph. The ship is moving due north at a speed of 18 mph. Find the direction of the woman relative to the surface of the water. Measure the angle from the positive -ais, and assume east points in the direction of the positive -ais. (a) arctan 6 (b) arctan 6 ( (c) arctan 1 ) 6 (d) arctan( 6) (e) arctan 1 3. Find the cosine of ABC for the points A(, 1), B(1, ), and C(0, ). (a) 3 10 (b) 6 5 17 (c) 5 34 (d) (e) 3 10 5 34 Page of 11
4. Find the vector projection of the vector, 4 onto the vector 5, 1. (a) 35 1, 7 1 7 (b) 5, 14 5 7 (c) 3, 14 3 (d) 35 13, 7 13 (e) 7, 7 10 5. Find the distance from the point (, 3) to the line y = 5 4 +. (a) 33 41 41 (b) 10 9 9 (c) 33 9 9 (d) 10 41 41 (e) 7 9 9 6. A sled is pulled along a level path by a rope. A 0-lb force acting at an angle of 30 above the horizontal moves the sled 7 ft. Find the work done by the force. (a) 70 J (b) 70 3 J (c) 140 J (d) 70 J (e) 35 J Page 3 of 11
7. Find parametric equations for the line through the point (, 9) that is parallel to the line 3+5y = 7. (a) = 5 + t, y = 3 9t (b) = + 3t, y = 9 + 5t (c) = + 5t, y = 9 3t (d) = + t, y = 5 9t (e) = + 5t, y = 5 + 7t 8. Simplify the epression tan (arccos()) (a) 1 (b) (c) 1 1 + 1 + (d) 1 1 (e) 9. Find the vertical asymptotes of the function f() = 5 3 10 (a) = only (b) = 5 only (c) = 0 only (d) = and = 5 (e) = 0, =, and = 5 Page 4 of 11
10. The following is the graph of a function y = f(). Which of the following statements concerning the graph is FALSE? (a) f() is not continuous at = 1 (b) f( 1) = 1 (c) f() is continuous from the left at = 1 (d) lim 1 f() does not eist (e) lim f() = 1 1 + 11. Evaluate lim 3 7 + 6 (a) 0 (b) 3 (c) 5 6 (d) (e) 1. Evaluate lim 3 + 3 4 1 (a) 1 10 1 (b) 10 (c) 0 (d) (e) Page 5 of 11
13. Evaluate lim ln ( 5 4 + 3 ) ln ( + 3 4) (a) 0 ( ) 5 (b) ln ( ) 5 (c) ln 3 (d) (e) 7 + 14. Evaluate lim 4 + 3 (a) 0 (b) 7 (c) 7 4 (d) 7 (e) 3e + 5e 7 15. Evaluate lim 4e 6e 7 (a) 0 (b) 5 6 (c) 3 4 (d) (e) Page 6 of 11
16. Which of the following statements is true regarding the equation 4 + 5 = 3? (a) A solution eists on the interval (0, 1) by the Squeeze Theorem (b) A solution eists on the interval (0, 1) by the Intermediate Value Theorem (c) A solution eists on the interval (1, ) by the Squeeze Theorem (d) A solution eists on the interval (1, ) by the Intermediate Value Theorem (e) The equation has no real number solutions. 17. Which of the following statements is true concerning lim sin? 0 (a) lim 0 sin (b) lim 0 sin (c) lim 0 sin (d) lim 0 sin (e) lim 0 sin = ) ( 1 does not eist since sin ( 1 ) is undefined at 0. does not eist since sin ( 1 ) oscillates as approaches 0. = 0 by the Intermediate Value Theorem since sin ( ) 1 = 0 by the Squeeze Theorem since sin ( ) 1 18. Determine { for what value of a, the following function is continuous everywhere. a f() = + 3 < a (a) 5 (b) 0 (c) - (d) 1 (e) No solution. Page 7 of 11
19. The displacement (in meters) of a particle moving in a straight line is given by s(t) = t 3t + 4, where t is measured in seconds. Find the average velocity over the interval [, 5]. (a) 4 m/s (b) 14 5 m/s (c) 4 3 m/s (d) 14 m/s (e) 9 5 m/s 0. The following is the graph of f (). Which of the following is the graph of f()? (a) (b) (c) (d) (e) Page 8 of 11
Part : Work out Directions: 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. 1. (5 pts each) Evaluate the following limits ( ) 4 3 5 (a) lim arctan 7 3 + 4 4 ( 4 (b) lim 5 5 ) 5 (c) ( lim ) 4 + Page 9 of 11
. (7 pts) Two forces F 1 and F act on an object. The magnitude of F 1 is 4 N and it makes a 10 angle with the positive -ais. The magnitude of F is 8 N and it makes a 45 angle with the positive -ais. Find the magnitude of the resultant force F. You must evaluate all trigonometric functions. You do not need to simplify the magnitude. 3. (8 pts) Consider the vector function r(t) = 1 + cos(t), + sin(t), where 0 t π. (a) Eliminate the parameter to find a Cartesian Equation. Your answer must NOT contain an inverse trigonometric function. (b) Sketch the curve on the grid below. Include the direction of the curve as t increases. Page 10 of 11
4. (10 pts) Use the definition of the derivative to find f () for f() = 7 +. No points will be given for any shortcut formulas used. FOR INSTRUCTOR USE ONLY Problem Points Awarded Points 1 0 60 1 15 7 3 8 4 10 Total 100 Page 11 of 11