m129SGFa10 - MATH 129 FINAL EXAM REVIEW PACKET (Revised...

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MATH 129 FINAL EXAM REVIEW PACKET (Revised Fall 2010) The following questions can be used as a review for Math 129. These questions are not actual samples of questions that will appear on the final exam, but they will provide additional practice for the material that will be covered on the final exam. When solving these problems keep the following in mind: Full credit for correct answers will only be awarded if all work is shown. Exact values must be given unless an approximation is required. Credit will not be given for an approximation when an exact value can be found by techniques covered in the course. The answers, along with comments, are posted as a separate file on http://math.arizona.edu/~calc. 1. Suppose the rate at which people get a particular disease (measured in people per month) can be modeled by ( ) 10 sin 30 3 rt t π  = +   . Find the total number of people who will get the disease during the first three months ( 03 t ≤≤ ). 2. If 3 1 () 7 f u du = , find the value of 2 1 (5 2 ) f x dx . 3. Evaluate 1 t dt t + 4. Use the method of integration by parts: a) Evaluate ( ) 2 2 ln 1 z dz z + b) Evaluate 2 arcsin( ) x x dx . c) Let g be twice differentiable with (0) 6 g = , (1) 5 g = , and 2 g = . Find 1 0 x g x dx ′′ . 5. Evaluate the following integrals (you can use the table of integrals): a) 2 cos (3 2) d θθ + b) 2 2 49 dt t c) 2 8 15 dy yy ++ 6. Use the method of partial fractions to evaluate 3 3 3 51 dy +− + .
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7. Use the method of trigonometric substitution to evaluate 2 32 (5 ) dx x . 8. The velocity v of the flow of blood at a distance r from the central axis of an artery with radius R is proportional to the difference between the square of the radius of the artery and the square of the distance from the central axis. Find an equation for v using k as the proportionality constant. Find the average rate of flow of blood. Recall that the average value of a function over [ a , b ] is given by 1 () b a f x dx ba . 9. In the study of probability, a quantity called the expected value of X is defined as ( ) E X xf x dx −∞ = . Find EX if 7 1 0 7 00 x ex fx x = < . 10. a) Find an approximation of 2 1 0 t e dt using the midpoint rule with 2 n = . (Show your work). b) Does the midpoint rule give an overestimate or underestimate for the integral in part a? 11. Determine if the improper integral converges or diverges. Show your work/ reasoning. If the integral converges, evaluate the integral. a) 2 0 1 4 dx x + b) 1 1 2 x dx c) ( ) 1 2 0 1 x x e dx e d) 2 6 sin cos x dx x π 12. According to a book of mathematical tables, 2 0 2 t e dt = . Use this formula and substitution to find 2 xm s m e dx    . Assume 0 s > . 13. Suppose f is continuous for all real numbers and that 0 f x dx converges. Determine which of the following converge. Explain or show your work clearly. Assume 0 a > .
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This note was uploaded on 02/04/2011 for the course MATH 9 taught by Professor Dwang during the Spring '08 term at University of Arizona- Tucson.

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m129SGFa10 - MATH 129 FINAL EXAM REVIEW PACKET (Revised...

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