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Unformatted text preview: MTH 230 COMMON FINAL EXAMINATION
YOUR NAME: __________________________ INSTRUCTIONS 1. Print your name and your instructor's name on this page using capital letters. Print your name on each page of the exam. Do not separate the pages of this exam. 2. This exam consists of this cover page and 9 additional pages containing 10 problems. Be sure your exam is complete before beginning work. Do not separate the pages of this exam. 3. Show your work. Work and/or explanation is required on all problems unless otherwise stated; if done well it may result in more credit. Answers accompanied by insufficient, unclear, or incorrect work may receive little or no credit. 4. The points assigned to a problem may not be distributed equally among the parts of a problem. 5. Do not use books, notes, papers, or other references. You may use a TI-81 through TI-86 or equivalent calculator. You are NOT permitted to use calculators capable of symbolic differentiation or integration (such as the TI-89, TI-92, or HP-48), portable computers, or any other device capable of storing or receiving information. 6. Do not submit scratch paper. Try to solve each problem in the space provided. If you need more space, use the back of this page or other blank space. Be sure to tell on the original page where your additional work can be found, and begin your additional work with the number of the problem being solved. INSTRUCTOR:__________________________ Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 TOTAL 20 30 15 15 20 20 20 20 15 25 200 MTH 230 Common Final Exam p. 1 of 9 Name _________________________________ (20) 1. In each part show complete details, including but not limited to an appropriate graph showing the region used to approximate the integral the numeric expression that you compute to get the answer (a) Use a Riemann sum with midpoints and n = 2 to approximate 0
4 x 3 + 1 dx . (b) Use the Trapezoidal Rule with n = 2 to approximate 0 4 x 3 + 1 dx . MTH 230 Common Final Exam p. 2 of 9 Name _________________________________ (30) 2. Evaluate the following integrals using symbolic methods. (a) 0p / 2 cos2 (x) dx (b) sin2 (x)cos(x)dx (c) x (x + 4)(x - 2) dx MTH 230 Common Final Exam p. 3 of 9 Name _________________________________ (15) 3. x Determine whether the integral 0 dx is convergent or divergent using symbolic 4 + x2 methods. If it's convergent, find the exact value. (15) 4. A bacterial population grows at a rate of 1000t e-t / 2 bacteria per hour. Find the total increase in the number of bacteria during the first two hours of growth. MTH 230 Common Final Exam p. 4 of 9 Name _________________________________ (20) 5. Determine the following limits. In each case your answer should be either an exact number, one of the symbols + or , or the phrase "does not exist". Show work or reasoning. (a)
x 0+ lim x ln(x) (b) x 0 lim cos(x) x2 MTH 230 Common Final Exam p. 5 of 9 Name _________________________________ (20) 6. A heavy metal chain weighs 1.5 pounds per foot, and 120 feet of the chain are hanging from the roof of a tall building. Find the work done pulling 60 feet of the chain up onto the roof. Give a brief explanation of your method. Be sure to specify the variable for vertical position. (Where is the vertical position zero? Which direction is positive, up or down?). MTH 230 Common Final Exam p. 6 of 9 Name _________________________________ (20) 7. m A particle moves with velocity function v(t) = t 2 - 4t + 3 sec during the interval 0 t 4. Its initial position is s(0) = 1 m . (a) Find the position function s(t) for 0 t 4 . (b) Find the displacement of the particle during the interval 0 t 4 . (c) Find the distance traveled during the interval 0 t 4 . MTH 230 Common Final Exam p. 7 of 9 Name _________________________________ (20) 8. Find the exact volume of the volume of revolution obtained by revolving about the line y = -1 the bounded region between the curves y = x 2 and y = 4x . MTH 230 Common Final Exam p. 8 of 9 Name _________________________________ (15) 9. dy = y 2 - x, y(0) = 0.3. dx Use Euler's Method with step size 0.5 to estimate y(0.5) and y(1.0). Consider the initial-value problem MTH 230 Common Final Exam p. 9 of 9 Name _________________________________ (25) 10. (a) "Radioactive substances decay at a rate proportional to the remaining mass". Use this principle to write a differential equation for the mass m(t) of a radioactive substance as a function of time. (b) Give the general solution to the differential equation you wrote in part (a). (No work required.) (c) It is known that radium-226 decays with a half-life of 1597 years. Suppose that a sample of radium-226 has an initial mass of 120 milligrams. Find an explicit formula for m(t), the mass of the remaining sample after t years. (d) After how many years will the mass of the sample be 100 milligrams? ...
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This note was uploaded on 05/03/2010 for the course CEG 260 taught by Professor Staff during the Spring '08 term at Wright State.
- Spring '08