Test 2 Version A. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test.

Transcription

1 Student s Printed Name: Instructor: CUID: Section: Instructions: You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop, tablet, SMART watch, or any technology on any portion of this test. All devices must be turned off while you are in the testing room. During this test, any communication with any person (other than the instructor or a designated proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity. No part of this test may be removed from the examination room. Read each question carefully. In order to receive full credit for the free response portion of the test, you must:. Show legible and logical (relevant) justification that supports your final answer. 2. Use complete and correct mathematical notation. 3. Include proper units, if necessary. 4. Give exact numerical values whenever possible. You have 9 minutes to complete the entire test. On my honor, I have neither given nor received inappropriate or unauthorized information at any time before or during this test. Student s Signature: Do not write below this line. Free Response Possible Points Free Response Possible Points Problem Points Earned Problem Points Earned. 4 5(a). 8 2(a). 8 5(b). 4 2(b). 8 5(c). 4 3(a). 4 Free Response 7 3(b). Multiple Choice 3 4. Test Total - Page of 2

2 Multiple Choice: There are multiple choice questions. They all have the same point value. Each question has one correct answer. The multiple choice problems will count for 3% of the total grade. Use a number 2 pencil and bubble in the letter of your response on the scantron sheet for problems -. For your own record, also circle your choice on your test since the scantron will not be returned to you. Only the responses recorded on your scantron sheet will be graded.. (3 pts.) Does the sequence whose nth term is a n = + ( )n n (a) Yes, it converges to -. (c) Yes, it converges to. converge? If so, to what value? (b) Yes, it converges to. (d) No, it diverges. 2. (3 pts.) Which of the following integrals is NOT improper? (a) 3 (x ) 2 dx (c) π/2 tan x dx (b) x x 2 dx (d) π/4 π/4 sec x dx - Page 2 of 2

3 3. (3 pts.) Consider the series k= ( 2 k + 2 ). Determine the partial sum S n for this series. k (a) S n = 2 n (c) S n = + 2 n + (b) S n = n + (d) S n = 2 2 n ( ) 2n 4. (3 pts.) Does the sequence whose nth term is a n = arctan converge? If so, to what + 2n value? (a) Yes, it converges to π 4. (c) No, it diverges. (b) Yes, it converges to. (d) Yes, it converges to π 2. - Page 3 of 2

4 7 5. (3 pts.) Is the series convergent or divergent? If it is convergent, what is the sum? 3n+ n= (a) convergent; sum = 7 2 (c) convergent; sum = 7 6 (b) divergent (d) convergent; sum = (3 pts.) Choose the correct partial fraction decomposition general form for the rational function x 3 + x (x 2 + 7x + 2)(x 2 + x + ) 2. (a) A x B x Cx + D x 2 + x + + Ex + F (x 2 + x + ) 2 (b) A x B x C x + + D (x + ) 2 + E (x + ) 3 + F (x + ) 4 (c) Ax + B x 2 + 7x Cx + D (x 2 + x + ) 2 (d) A x B x C x 2 + x + + D (x 2 + x + ) 2 - Page 4 of 2

5 7. (3 pts.) Consider the curve defined by y = x + for x 3. Which of the following gives the area of the surface obtained by rotating the curve on the given interval about the x-axis? (a) 3 4x + 5 2πx 4x + 4 dx (c) 3 x + 2 2πx x + dx (b) 3 2π 4x + 5 x + 4x + 4 dx (d) 3 2π x + x + 2 dx 8. (3 pts.) For which of the following integrals is integration by parts the best technique to use? ln x (a) x dx (c) x 2 e 3x dx (b) 2xe x2 dx (d) x x 2 + dx - Page 5 of 2

6 9. (3 pts.) Does the sequence whose nth term is a n = 4 sin n n 3 (a) Yes, it converges to 4. (c) No, it diverges. converge? If so, to what value? (b) Yes, it converges to. (d) Yes, it converges to.. (3 pts.) Using the Comparison Test, the series (a) Diverges because k= k 3/2 + : k 3/2 + < k 3/2 and diverges. k3/2 k= (b) Converges because k 3/2 + > k 3/2 and converges. k3/2 k= (c) Diverges because k 3/2 + > k 3/2 and diverges. k3/2 k= (d) Converges because k 3/2 + < k 3/2 and converges. k3/2 k= - Page 6 of 2

7 Free Response. The Free Response questions will count for 7% of the total grade. Read each question carefully. To receive full credit, you must show legible, logical, and relevant justification which supports your final answer.. (4 pts.) Evaluate 5x 2 4x + 8 x 2 (x 2 + 4) dx. - Page 7 of 2

8 2. Determine whether each of the following series converges or diverges. Remember to include the name of the convergence test used, work to show that the test conditions have been met, and a conclusion statement about convergence or divergence of the series. (a) (8 pts.) n= 2n 5 + n (b) (8 pts.) n= n (n 2 + ) 2 - Page 8 of 2

9 3. (4 pts.) Consider the infinite series: n= 3 2n +. (a) (4 pts.) Show the conditions are met for the Integral Test. (b) ( pts.) Use the Integral Test to determine if the series converges or diverges. - Page 9 of 2

10 4. ( pts.) Determine whether the following integral is convergent or divergent. Evaluate the integral if it is convergent. x ln x dx - Page of 2

11 5. (6 pts.) (a) (8 pts.) Find the arc length of the curve x = 3 (y2 + 2) 3/2 for y 2. (b) (4 pts.) Consider the curve defined by y = e 2x, x. Set up but do not evaluate or simplify an integral with respect to x representing the area of the surface obtained by rotating the curve on the given interval about the y-axis. (c) (4 pts.) Consider the curve defined by x = tan y, y π/4. Set up but do not evaluate or simplify an integral with respect to y representing the area of the surface obtained by rotating the curve on the given interval about the y-axis. - Page of 2

12 Scantron: Check to make sure your Scantron form meets the following criteria: My Scantron: is bubbled with firm marks so that the form can be machine read; is not damaged and has no stray marks (the form can be machine read); has bubbled in answers; has MATH 8 and my Section number written at the top; has my Instructor s last name written at the top; has Test No. 2 written at the top; has the correct test version written at the top and bubbled in below my XID; shows my correct XID both written and bubbled in. **Bubble a zero for the leading C in your XID**. - Page 2 of 2