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Unformatted text preview: Math 122 Final December 11, 2007 SI: Name 1 /20 2 /20 3 /20 4 /20 5 /20 6 /20 7 /20 8 /20 9 /20 10 /15 Style /5 Total /200 Directions: 1. No books, notes or whining about the weather. You may use a cal culator to do routine arithmetic computations. You may not use your calculator to store notes or formulas. You may not share a calculator with anyone. 2. You should show your work, and explain how you arrived at your an swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. 3. You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or you will be penalized. 4. You may leave as soon as you are finished, but once you leave the exam, you may not make any changes to your exam. Have a Safe and Happy Break 1. (20 points) (a) Compute Z x 4 1 x dx Hint: Z u 2 a 2 u = u 2 a 2 a sec 1 u a + C (b) Compute Z 1 x ln x ((ln(ln x )) dx (c) Compute Z arcsin x dx . (d) Compute Z sin 2 x cot 2 x dx 2. (20 points) (a) Compute Z x x 2 + 3 x + 2 dx . (b) Compute Z 1 ( x 2 + 9) 3 / 2 dx (c) Compute Z 1 9 x 2 + 6 x + 5 dx . (d) Compute 3 Z 1 1 ( x 2) 3 dx 3. (20 points) (a) For the differential equation dy dx = F ( x,y ), where F ( x,y ) is given below: x 1 2 3 4 111 11 1 1 1 y 2111 3 1 111 4 1 1 i. Use Eulers method with h = 1 and y (0) = 2 to approximate y (4). ii. Sketch the slope field at the given points. (b) Find the general solution for the following differential equations. i. dy dx = x 2 y 2 + x 2 + y 2 + 1 ii. dy dx 2 xy = 2 xe 2 x 2 4. (20 points) Prof. Kenney is really hungry but he is on a diet. He decides to eat a hamburger/Diet Coke pur ee (Yum). His stomach originally contains 100 Liters of pure Diet Coke (no hamburgers). He drinks 10 Liters of hamburger/Diet Coke pur ee per minute that contains 4 hamburgers per Liter and the mixed solution leaves his stomach at the...
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This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.
 Spring '07
 Butler
 Math

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