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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.
 Spring '07
 Hamilton
 Math

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