Exam_exam_2_(2)

Exam_exam_2_(2) - g . What is ( ) 1 g ′ ? 2. (14 points)...

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Math 141, Sections 03**, T Pilachowski, Spring 2007 March 2, 2007 MATH 141 – TEST 2 (7.1 – 7.8) [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) Let () 7 18 3 2 2 3 + + = x x x x f and Let [ a , b ] be the largest interval containing x = 0 such that f has an inverse function 1 f on this interval. Find a and b . (You must show calculus work.) b. (4 extra points) You know that g (1) = 2, and ( )() 3 2 1 =
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Unformatted text preview: g . What is ( ) 1 g ′ ? 2. (14 points) Use integration by substitution to evaluate ∫ − 3 2 2 cos 1 2 sin 2 π dx x x . 3. a. (14 points) Find the slope of the curve x y x 2 log 2 − = at x = 2. Give an exact value answer in simplest form. b. (14 points) Find ( ) x x e x x 1 lim + → . Possible answers are a calculated numeric value, , , ∞ ∞ − or DNE (does not exist). You must show all your steps in order to receive full credit. 4. a. (14 points) Solve the initial value problem 2 1 2 , cos 3 4 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = + ′ y t y y . b. (10 points) Sketch the direction field of the differential equation y t y 2 − = ′ . Use the nine points pictured to the right. → 5. a. (14 points) Solve the differential equation x x y y cos cos = + ′ . b. (8 points) Verify that the solution you found in 5.a. is a correct general solution to the differential equation x x y y cos cos = + ′ ....
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This note was uploaded on 09/07/2011 for the course MATH 141 taught by Professor Hamilton during the Spring '07 term at Maryland.

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