sample_test2-1

sample_test2-1 - 2 . 1 (Hint: What value of x should you...

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SAMPLE TEST 2 VERSION A On all problems, you must show your work to receive credit. 1. (25 points) a) Sum the series 5 / 3 - 5 / 9 + 5 / 27 - 5 / 81 + .... 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 70% of the amount present in the body. In the long run, the doctor would like the amount of drug in the body, immediately after taking a dose, to approach 6 mgs. What should D be? 2. (25 points) a) Find the third Taylor Polynomial of 3 x - 1 at x = 2. b) Use a) to approximate 3
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Unformatted text preview: 2 . 1 (Hint: What value of x should you use?). 3. (25 points) a) Using the Taylor series sin x = x-x 3 3! + x 5 5!-... , nd the rst three nonzero terms of the Taylor series of sin(2 x ) 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 x 2-1 x dx 4. (25 points) a) Evaluate Z R Z e 2 x-y dxdy where R is the region bounded by x = 0 ,x = 1 ,y = 0 , and y = 2. b) Evaluate Z 1 ( Z y 2 y 2 x + xy 2 dx ) dy...
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