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Final Fall 2006

# Final Fall 2006 - Math 122 Final 1 Name 2 3 4 5 6 7 8 9 10...

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Math 122 Final December 12, 2006 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 book, notes, loud snoring, steriods, or delinquent activities. 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. (20 points) (a) Use the formula: Z du u 2 u 2 ± a 2 = u 2 ± a 2 a 2 u + C to evaluate Z 1 x 2 4 x 2 + 9 dx (b) Z 4 x (1 + x 2 ) 2 dx (c) Z ln x x 2 dx (d) Z cos 2 x sin x dx
2. (20 points) (a) Z tan 3 x sec x dx (b) Z 5 2 x 2 - 3 x - 2 dx (c) Z 1 9 x 2 + 6 x + 5 dx (d) Z x 3 1 - x 2 dx

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3. (20 points) (a) Use Euler’s method with h = 0 . 50 to approximate y (1) for the initial value problem dy dx = x + 2 y y (0) = 1 (b) Find the general solution for the following differential equation: (1 + x 2 ) 2 dy dx = 4 xy (c) Find the general solution for the following differential equation: dy dx - 3 y = e 3 x sin x
4. (20 points) (a) The country of New Zealand has \$ 300 million in paper currency in circulation and each day \$ 15 million comes into (and out of) the country’s bank. The government decided to introduce new currency featuring a certain Chemistry Professor because a smaller portrait was needed. The banks will replace old bills with new ones, whenever old currency comes into the bank. Let y = y ( t ) denote the amount of new currency in circulation at time t , with y (0) = 0.

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Final Fall 2006 - Math 122 Final 1 Name 2 3 4 5 6 7 8 9 10...

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