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Final Fall 2008 - Math 122 Final December 9 2008 SI 1 2 3 4...

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Math 122 Final December 9, 2008 SI: Name 1 /15 2 /15 3 /15 4 /15 5 /15 6 /15 7 /15 8 /15 9 /15 10 /15 11 /15 12 /15 13 /15 Style Points /5 Total Directions: 1. No book, notes, or hiding extra salad dressing in your pocket. You may use a calculator 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.
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1. (15 points) (a) Z x 1 + x 4 dx (b) Use the formula: Z u 2 ± a 2 du = u 2 u 2 ± a 2 ± a 2 2 ln u + u 2 ± a 2 + C to evaluate Z e x 9 + e 2 x dx (c) Z x 3 ln x dx
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2. (15 points) (a) Z tan 3 x sec 3 x dx (b) Z 1 (9 - x 2 ) 3 / 2 dx (c) Z 1 sec 2 x dx
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3. (15 points) (a) Z 4 x 2 - 3 x - 4 x 3 + x 2 - 2 x dx (b) Z 1 4 x 2 + 4 x + 2 dx
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4. (15 points) (a) Solve the initial value problem dy dx = 3 x 2 y 2 - y 2 y (0) = 1 (b) Find the general solution for the following differential equation: x dy dx - 5 y = x 6 cos x
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5. (15 points) At time t = 0, a tank contains 10 lbs. of chocolate syrup in 100 gallons of milk. Suppose that chocolate milk containing 2 lbs of chocolate syrup per gallon of milk is allowed to enter the tank at a rate of 5 gal/min and the mixed solution is drained from the tank at the same rate. (a) Write a differential equation (with initial condition) for how much chocolate syrup is in the tank?
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