Download Exam Questions: Mathematics - Polar Coordinates, Integration, Partial Fractions, Sequences and more Exams Calculus in PDF only on Docsity! You scored 30 out of 30 Question 1 Your answer is CORRECT. Write the given equation in rectangular coordinates: a) b) c) d) e) Question 2 Your answer is CORRECT. Which of the following shows the correct sketch of the given polar curve? You may use the following table to help with your calculations: θ π/6 π/4 π/3 sin(θ)θ) 0.5 0.7 0.87 cos(θ)θ) 0.87 0.7 0.5 oy
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a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 6 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 616 Given x f (θ)x) 0 3 0.5 2 1 -4 1.5 -7 2 5 2.5 9 3 -6 3.5 -5 4 -8 4.5 5 5 -7 and the integral Part a: Use the trapezoid method with n = 3 to approximate the integral. Part b: Use the midpoint method with n = 3 to approximate the integral. Part c: Use Simpson's rule with n = 3 to approximate the integral. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 7 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 719 Part a: Give a partial fraction decomposition for . Part b: Suppose you know the partial fraction decomposition of is . Compute: a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 8 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 816 Part a: Set up the integral needed to compute using trigonometric substitution. DO NOT EVALUATE THE INTEGRAL. Part b: Suppose that the trigonometric substitution x = 4tanu is used to compute an integral and the answer to the integral is Finish the problem by rewriting the answer in terms of x. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 9 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 911 Part a: Determine whether the following set is bounded below. If it is bounded below, identify the greatest lower bound. {x : x2 < 9} Part b: Assume the following sequence begins with n = 1. Determine the boundedness and monotonicity of this sequence. Part c: Assume the following sequence begins with n = 1. Determine the boundedness and monotonicity of this sequence. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 10 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1022 For each of the following, state whether the sequence converges or diverges. If the sequence converges, find the limit. If the sequence diverges, explain why. Part a: Part b: Part c: a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.
