Exam 3 - Fall 2005

Exam 3 Fall 2005 - 29 1 = y x y Leave your answer in implicit form b Find the particular solution of the differential equation above that satisfies

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Calculus I, Exam #3 Fall 2005 Primarily Chapters 4 and 5 Name____________________________ Please show all work to receive full credit. Answers without appropriate supporting work will not receive credit. Each problem is worth 10 points. Give exact answers unless indicated otherwise. 1. Evaluate the integrals a. dx x x + 2 3 4 3 b. xdx x 2 sec tan 2. Evaluate dx x x + + 9 16 5 2

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3. Use the limit process to find the area of the region between 1 2 ) ( 2 - = x x f and the x-axis over the interval [0,1]. = x = i c 4 Evaluate: a. dx x + 2 2 2 b. ( 29 dt t t dx d x 4 0 2 2 - 5. A certain type of bacteria increases continuously at a rate proportional to the number present. If there are 500 present at a given time and 1000 present 2 hours later, how many will there be 5 hours from the initial time given? (Find the growth function and show all work) (Round your answer to 3 decimal places.)
6. a. Solve the separable differential equation

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Unformatted text preview: ( 29 ' 1 = + + y x y . Leave your answer in implicit form. b. Find the particular solution of the differential equation above that satisfies the initial condition 1 ) 2 ( =-y 7. Solve the first-order linear differential equation 3 2 3 ' x e y x y =-8. a. Evaluate the following dx x x ∫ + 2 b. Find dx dy for x x x y sinh cosh-= 9. a. Find the average value of x x f sin ) ( = on the interval 2 , 4 π b. dx x ∫--3 1 3 1 2 9 4 3 10. a. Use the definition of derivative to find ) ( ' x f for 1 1 ) (-= x x f b. A balloon rises at the rate of 8 feet per second from a point on the ground 60 feet from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground....
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This note was uploaded on 01/12/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.

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Exam 3 Fall 2005 - 29 1 = y x y Leave your answer in implicit form b Find the particular solution of the differential equation above that satisfies

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