MATH Exam 2-3/10/2017
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1 MATH 1 - Exam - 3/10/017 Name: Section: Section Class Times Day Instructor Section Class Times Day Instructor 1 0:00 PM - 0:50 PM M T W F Daryl Lawrence Falco 11 11:00 AM - 11:50 AM M T W F Hwan Yong Lee 09:00 AM - 09:50 AM M T W F Robert Immordino 13 10:00 AM - 10:50 AM M T W F Marci Ann Perlstadt 3 1:00 PM - 1:50 PM M T W F Marci Ann Perlstadt 14 1:00 PM - 1:50 PM M T W F Hwan Yong Lee 4 10:00 AM - 10:50 AM M T W F Robert Immordino 15 04:00 PM - 04:50 PM M T W F Dennis Guang Yang 5 10:00 AM - 10:50 AM M T W F Matthew J Ziemke 16 1:00 PM - 1:50 PM M T W F Dennis Guang Yang 6 01:00 PM - 01:50 PM M T W F Hwan Yong Lee 17 10:00 AM - 10:50 AM M T W F Daryl Lawrence Falco 8 11:00 AM - 11:50 AM M T W F Matthew J Ziemke 18 01:00 PM - 01:50 PM M T W F Dennis Guang Yang The following rules apply: General rules: This is a closed-book exam. You may not use any books or notes on this exam. You have 50 minutes to complete this exam. When time is called, stop writing immediately and turn in your exam to the nearest proctor. You may not use any electronic devices including (but not limited to) calculators, cell phone, or ipods. Using such a device will be considered a violation of the university s academic integrity policy and, at the very least, will result in a grade of 0 for this exam. For free response questions: You must show all work. Answers without proper justification will not receive full credit. Partial credit will be awarded for significant progress towards the correct answer. Cross off any work that you do not want graded. Page Points Score Total: 100 For multiple choice questions: Circle the letter of the best answer. Make sure your circles include just one letter. These problems will be marked as correct or incorrect; NO partial credit will be awarded for problems in this section.
2 MATH 1 Exam - Page of 10 3/10/017 Part I: Free Response 1. (15 points) Evaluate the definite integral. π/6 0 x cos(x) dx
3 MATH 1 Exam - Page 3 of 10 3/10/017. (15 points) Determine whether the integral converges. If so, evaluate it. 1 dx x + x
4 MATH 1 Exam - Page 4 of 10 3/10/ (15 points) Solve the initial value problem. Express your solution as an explicit function of x. dy dx = xex y, y(0) = 3
5 MATH 1 Exam - Page 5 of 10 3/10/ (15 points) Evaluate the integral. sin 4 x cos 5 x dx
6 MATH 1 Exam - Page 6 of 10 3/10/ (15 points) A tank has the shape of an inverted circular cone with a height of 10 feet and radius of 4 feet. If the tank is filled to a height of 8 feet with a liquid having a weight density of 50 lb/ft 3, set up but do not evaluate the integral that represents the work required to empty the tank by pumping all of the liquid to the top of the tank
7 MATH 1 Exam - Page 7 of 10 3/10/017 Part II: Multiple Choice 6. (5 points) If the work required to stretch a spring 4 feet beyond its natural length is 80 ft-lb, which of the following integrals represents the work (in ft-lbs) needed to stretch the spring 6 inches beyond its natural length? Hint : 1 foot = 1 inches. (a) (b) (c) (d) (e) x dx 10x dx 0x dx 0x dx 0x dx 7. (5 points) With the trigonometric substitution x = tan θ, π < θ < π, the integral converts to which of the following integrals? (a) tan θ dθ (b) tan θ sec θ dθ (c) tan θ sec θ dθ x 1 + x dx (d) (e) tan θ sec θ dθ tan θ sec θ dθ
8 MATH 1 Exam - Page 8 of 10 3/10/017 [ 8. (5 points) Consider the curve defined by y = sin x on π 3, π ] or, equivalently, x = sin 1 y on [ ] 4 3,. Which of the following integrals represents the arc length of the curve? (a) (b) (c) (d) (e) π/4 π/3 π/4 π/3 / 3/ / 3/ / 3/ 1 + sin x dx 1 cos x dx y dy 1 + y dy y dy 9. (5 points) Consider the following partial fraction decomposition. Find the values of A, B, and C. x + x 8 x 3 + 4x = A x + Bx + C x + 4 (a) A =, B = 3, and C = 1 (b) A =, B = 3, and C = 1 (c) A =, B = 4, and C = 1 (d) A =, B = 4, and C = 1 (e) A =, B = 4, and C =
9 MATH 1 Exam - Page 9 of 10 3/10/ (5 points) Evaluate the following integral (x 1) dx (a) 0 (b) (c) (d) + (e)
10 MATH 1 Exam - Page 10 of 10 3/10/017 sin x + cos x = 1 tan x + 1 = sec x sin x = 1 cos(x) cos x = 1 + cos(x) sin(x) = sin x cos x cos(x) = 1 sin x = cos x 1 sin A cos B = 1 [sin(a B) + sin(a + B)] sin A sin B = 1 [cos(a B) cos(a + B)] cos A cos B = 1 [cos(a B) + cos(a + B)]
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