MATH 151, SPRING 2018

Transcription

1 MATH 11, SPRING 018 COMMON EXAM I - VERSIONAKEY 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! 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.. Be sure to write your name, section number and version letter of the exam on the ScanTron form. 6. Again. The use of a calculator, laptop or computer is prohibited. THE AGGIE HONOR CODE An Aggie does not lie, cheat, or steal, or tolerate those who do. Signature: 1

2 FOR INSTRUCTOR USE ONLY Question Points Awarded Points TOTAL 100

3 Part 1: Multiple Choice (3 points each) 1. Which of the following vectors is perpendicular to the line 3x y = 10. (a) 1,3 (b) 1, (c) 3,1 (d) 10, (e) 6, key A f(x). Given that lim f(x) = 3 and lim g(x) = 0, find lim x a x a x a g(x) f(x). (a) 3 (b) key A (c) 0 (d) (e) 3 3. Use the Intermediate Value Theorem to determine which function has a solution to the equation f(x) = 1 on the interval (0, 1)? (a) f(x) = x 3 +x (b) f(x) = x 4 x 3 +1 (c) f(x) = x +x (d) f(x) = x 6 4x +1 key A (e) None of these 4. Given a = 3, 1 and b = 1,7, find the scalar projection of b onto a. (a) key A (b) 3i+j (c) i 7j (d) 10 0 (e) 1 3

4 . Consider the triangle with vertices A(3,0), B(4,3), and C( 1,1). Find the measure of angle ABC. ( (a) ABC = arccos 1 ) 90 ( ) 11 (b) ABC = arccos 41 ( (c) ABC = arccos 1 ) 41 ( ) 11 (d) ABC = arccos key A 90 ( ) 13 (e) ABC = arccos Given f(x) = x 7, which statement is true when x = 7? (a) f is differentiable at x = 7. (b) f is not differentiable at x = 7 because lim x 7 f(x) does not exist. f(x) f(7) (c) f is not differentiable at x = 7 because lim does not exist. key A x 7 x 7 (d) f is not differentiable at x = 7 because lim f(x) exists but does not equal f(7). x 7 (e) None of the other statements are true. 7. Given that x 3 3x+4 f(x) 3x +6x 1 on the interval [,], which of the following is correct regarding lim x 1 f(x)? (a) lim f(x) = by the Squeeze Theorem. key A x 1 (b) lim f(x) = by the Intermediate Value Theorem. x 1 (c) lim f(x) = 0 by the Squeeze Theorem. x 1 (d) lim f(x) = 0 by the Intermediate Value Theorem. x 1 (e) None of these. 4

5 8. Find a vector of length in the same direction as the vector from the point ( 1,) to (,6). 3 (a), 4 (b) 3,4 key A (c) 3, 4 (d) 3, 4 (e) 3, 4 9. Evaluate lim t 6t +3t (3 t)(t+4) (a) 3 (b) 0 (c) 6 (d) (e) 3 key A 10. Here is the graph of a function f(x). Which of the following is false? y x (a) f(x) is continuous from the left at x = 1 (b) f(1) = (c) lim x f(x) = 3 (d) f(x) has a removable discontinuity at x = (e) lim x 1 f(x) = key A

6 11. Find the distance from the point P(1,7) to the line x y = 6. (a) (b) 9 (c) 1 (d) 11 key A (e) 3 3x+ 1. Compute lim x 4x +x+1 (a) 3 (b) (c) 3 key A (d) 3 4 (e) 0 6e x 8e 3x 13. Compute lim x 3e x +e 3x (a) (b) 8 3 (c) (d) 4 key A (e) 14. Simplify tan(arccos x) to an algebraic expression. (a) (b) 1 x key A x x 1 x (c) 1 x x (d) 1+x (e) 1 1+x 6

7 1. Find the average rate of change of f(t) = t+3 from t = 1 to t = 3. (a) 3 (b) 3+ 3 (c) (d) 3+ (e) 3 key A 16. A wagon is pulled a distance of feet along a horizontal path by a constant force of 8 pounds. The handle of the wagon is at an angle of 60 above the horizontal. How much work is done? (a) ft lbs (b) 100 ft lbs (c) 00 ft lbs (d) 100 ft lbs key A (e) 00 3 ft lbs x +3x 17. Compute lim x 3 x x 1 (a) 0 (b) 3 7 key A (c) 1 (d) 3 (e) None of these 7

8 18. Find the value of a that makes f(x) = (a) 3 17 (b) 0 (c) 3 key A (d) 1 (e) Does not exist { x+8a if x < 3 ax continuous everywhere. if x 3 x Evaluate lim x 3 x 4x+3. (a) 1 (b) 1 (c) 0 (d) 1 key A (e) None of these 1 if x < 1 x 0. Given g(x) = 4x if 1 x < 0. Which statement is true? e x if x 0 (a) g(0) is undefined, thus g(x) is discontinuous at x = 0 (b) lim x 0 g(x) exists and g(0) is defined, but lim x 0 g(x) g(0), thus g(x) is discontinuous at x = 0 (c) lim x 0 g(x) does not exist, thus g(x) is discontinuous at x = 0 key A (d) g(x) is continuous at x = 0 (e) None of the above 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. (1 pts) Evaluate these limits. Do not use the L Hospital method. ( 1 (a) lim x x 4 ) x 4 key: 1 4 (b) lim x ( x +4x+ x). key: (c) lim x 8x+1 key: x 3 x+ 9

10 . (10 pts) A boat heads in the direction N30 E with a speed of 40mph. The water current is flowing S4 E with a speed of 6mph. Find the true speed of the boat. (Do not simplify but evaluate all trigonometric function values) 30 4 key: (0+3 ) +(0 3 3 ) 3. (8 pts) Consider the vector function r(t) = 3+cost, 1+sint, 0 t π (a) Eliminate the parameter to find a cartesian equation. Your answer must NOT be in terms of inverse trigonometric functions. key : (x 3) +(y +1) = 1 (b) Sketch the curve on the grid below. Include the DIRECTION of the curve as t increases. 4 y 3 1 x

11 4. (10 pts) Using the definition of the derivative, find f (x) for f(x) = 3x 4x+. key: f (x) = 6x 4 11