Math 132 Final Exam Fall 2018 Name Signature Student ID Number Section Number Section Instructor Day Time Section Instructor Day Time MWF 9 05 1 6 MWF 10 10 7 2 MWF 11 15 8 3 4 MWF 12 20 9 5 Correia Correia Duan Nguyen Hacking MWF 1 25 TuThu 1 00 Farelli Farelli TuThu 2 30 Destromp MWF 10 10 MWF 1 25 Torres Dul MWF 8 00 Nakamura TuThu 8 30 10 11 No calculator papers phones smart watches or notes may be used In the free response section do not just give an answer Clearly explain how you get it providing appropriate mathematical details An answer with no relevant work will be awarded zero points This is a 2 hour exam Question Multiple Choice Questions Out of 25 6 Out of 10 Grade 7 Out of 10 8 Out of 10 9 Out of 10 10 Out of 10 11 Out of 10 12 Out of 15 Total Out of 100 Multiple Choice Section Choose the one option that answers the question There is no partial credit for questions 1 5 Only answers written in the answer blank will be graded 1 5 points Calculate the following derivative 6 0 sin A 6 5 sin 6 B cos 6 1 C cos 6 Answer 1 D sin 6 2 5 points Given the parametric equations below calculate the second derivative 2 2 at the point A 3 B 1 4 C 4 D 2 Answer 2 cos 2 sin At 6 2 3 5 points Which of the following integrals represents the area between the curves 6 2 2 and 1 2 1 2 3 2 2 A 6 2 2 2 B 6 2 2 2 C 6 0 3 2 2 Answer 3 D There is not enough information to calculate the area between the curves 5 points Find the Polar equation for the following Cartesian equation 15 A 15cos 15 sin B C D 15 sec 15 csc Answer 4 4 3 5 5 points Find the radius of convergence for the following series 0 9 2 5 A 5 B C D 1 5 9 1 Answer 5 4 Free Response Section Show all work for each of the following questions Partial credit may be awarded for questions 6 12 6 10 points Evaluate the integral 2 tan 8 cos2 5 7 10 points The Maclaurin series for is given below Use a Maclaurin series to evaluate the following integral 0 7 3 3 6 8 10 points Express the function as a power series Express your answer in summation notation and simplify completely within the summation 3 4 1 2 2 7 9 10 points Find the interval of convergence for the following series 1 2 3 3 4 0 8 10 10 points Find a Taylor series for the function below Express your answer in summation notation and simplify completely within the summation 5 2 Centered at 2 9 11 Consider the curve defined by the parametric equations below sin 2 cos 0 a 5 points Find the point s where the curve has a vertical tangent line b 5 points Set up but do not evaluate a definite integral representing the exact length of the curve 10 12 a 10 points Find the area enclosed by one loop the polar equation sin 5 The graph for this equation is given below y b 5 points Find for the polar equation sin 5 11