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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 ith 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 212) (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 minimum, or neither....
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 Spring '08
 Hotlz
 Math, Calculus, Critical Point, Optimization, Fermat's theorem

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