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fx165f2009_2

# fx165f2009_2 - ∑ n i =1 f x i)Δ x where x i is the right...

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Math 165 Final Exam, Fall 2009 Second Part Name : Section: Answer each question completely. Show all work. No credit is allowed for mere answers with no work shown. Show the steps of calculations. State the reasons that justify conclusions. 1. (10 points) Find the particular solution to the differential equation dy/dx = - yx ( x + 2) that passes through (0, 20).

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2. (10 points) Tina has a corner of her house that she would like to fence in for her rabbits, using 20 feet of fence. Two sides of the pen will be the sides of her house which are longer than 20 feet. The sides of the pen along the house need no fence. See the figure. What are the dimensions of the pen that maximizes the perimeter of the pen?
3. (10 points) Calculate the definite integral of the function f ( x ) = x 2 over the interval [0 , 2] by following the steps: i) subdivide the interval into n subintervals of equal length Δ x , ii) form the sum

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Unformatted text preview: ∑ n i =1 f ( x i )Δ x , where x i is the right end point of the i-th subinterval, iii) evaluate the sum using the fact that ∑ n i =1 i 2 = n ( n + 1)(2 n + 1) / 6, and iv) compute the limit of the sum as n → ∞ . 4. (12 points) A balloon leaving the ground 1200 ft from an observer rises vertically at the rate of 200 ft/min. How fast is the angle of elevation of the observer’s line of sight increasing when the balloon is at an altitude of 1600 ft? (Simplify your answer, and be sure to include the units.) 5. (10 points) Consider the function g ( x ) = e 2 x ( x 2-12) (a) Find all x such that g ( x ) = 0. (b) Find all critical points of this function. (c) On what intervals is g increasing? On what intervals is g decreasing? (d) Determine for each stationary point whether it is a local maximum, a local mini-mum, or neither....
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fx165f2009_2 - ∑ n i =1 f x i)Δ x where x i is the right...

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