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Exam_exam_4_ - MATH 141 TEST 4(9.1 9.9[Pilachowski Follow...

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April 27, 2007 MATH 141 – TEST 4 (9.1 – 9.9) [Pilachowski] Follow directions carefully: Use exactly ONE answer sheet per question (use the back of the sheet if needed). Put your name, your TA's name and the question number on EACH page. No books, notebooks, calculators, cell phones or other electronic devices. Put a BOX around the final answer to a question. Show enough work that we can follow your thinking. You must show all appropriate work in order to receive full credit for an answer. Answers should always be in simplest form. Before handing in your test: on your first answer sheet only, please copy the pledge and sign. 1. a. (12 points) Use derivatives to find the 4th Taylor polynomial ( ) x p 4 about x = 0 for the function . (You must show your steps to receive full credit.) ( ) x e x f 2 = b. (10 points) Find the sum of the series = + + 0 3 2 1 2 3 n n n . c. (4 extra points) The sequence 0 tan 1 1 = n n converges to what value?
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