sample_test2_B

sample_test2_B - x should you use?) 3. (25 points) a) Using...

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SAMPLE TEST 2 VERSION B On all problems, you must show your work to receive credit. 1. (25 points) a) Sum the series 3 / 4 - 3 / 16 + 3 / 64 - 3 / 256 + .... b) A doctor wishes to give a patient a daily dose of D mgs of a certain medicine. The doctor knows that the body eliminates each day 60% of the amount present in the body. In the long run, the doctor would like the amount of drug in the body, after a dose is taken, to approach 6 mgs. What should D be? 2. (25 points) a) Find the third Taylor Polynomial of 3 x - 2 at x = 3. b) Use a) to approximate 3 1 . 5. (Hint: What value of
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Unformatted text preview: x should you use?) 3. (25 points) a) Using the Taylor series cos x = 1-x 2 2! + x 4 4!-x 6 6! + ... , nd the rst three nonzero terms of the Taylor series of cos(3 x )-1 x . b) Given that e x = 1+ x + x 2 2! + x 3 3! + ... , nd the rst three nonzero terms of an innite series converging to Z 1 e 2 x-1 x dx 4. (25 points) a) Evaluate Z R Z e 2 y-x dydx where R is the region bounded by x = 0 ,x = 1 ,y = 0 , and y = 2. b) Evaluate Z 1 ( Z y 2 y x + xydx ) dy...
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