Quiz-1-s11 - ! where ! ! is a given well-behaved function...

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1 AMS 361: Applied Calculus IV by Prof. Y. Deng Quiz 1 Wednesday (03/09/2011) at 3:50PM-5:10PM in 137 Harriman (1) Closed Book with 1-page (double-sided 8.5x11) formulas. (2) Do any two of the three problems. If all three are attempted, the two best (and only two) will be graded. (3) Each problem is worth 5 points. (4) No points for guessing work and for solutions without appropriate intermediate steps; Partial Credits are Given only for Steps that are Relevant to the solutions. SB ID: Class ID: Name: Problems To Grade? Score Remarks Q1-1 Q1-2 Q1-3 Total Score Q1-1 (5 points): It is obvious that ! = ! satisfies the following DE. With this info, find its general solution !" !" = ! ! + ! + ! !
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Unformatted text preview: ! where ! ! is a given well-behaved function and a is a given constant. Q1-2 (5 points): Find the general solution of the following DE: ! ! 2 !" + 1 = 2 ! ! ! Q1-3 (5 points): Consider shooting, at an initial speed ! ! , a bullet of mass ! to a medium whose resistance is ! ( ! + ! ! ) where ! is the instatenous speed, ! is the given resistance constant and ! is another given constant. You may assume the medium infinite (for example, the ocean) and you may also neglect the gravity for this problem. Please (a) Compute the farthest distances the bullet can travel in the medium and (b) the time the bullet is in motion. (2.5 points/question)....
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