MATH 140 Dec 2007 Answers

MATH 140 Dec 2007 Answers - Q1 (a) Q2 (a) Q3 (a) 1 , (b) 2...

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Q1 (a) - 1 2 , (b) 1 3 , (c) - π 2 , (d) 1 3 , (e) - 5 2 . Q2 (a) y = π - 1 , y = - π - 1 , (b) x = - 2 , x = 2 , (c) 5 288 π cm/s. Q3 (a) e x , (b) - u 1 - u 2 , (c) - 2 + cosh( x ) , (d) 14 25 . Q4 (a) When x = - 1 , y = - 6 . When x = 0 , y = 1 . Since y depends continuously on x , by the Intermediate Value Theorem, y must vanish at least once in - 1 < x < 0 . On the other hand y 0 = 2 + 3 x 2 + 20 x 4 2 . If y were to vanish at two distinct points x = a and x = b , then by Rolle's Theorem, y 0 would vanish at some point between a and b . It doesn't. Hence there is at most one solution in x to the equation y = 0 . (b) K = 2 . Q5 At x = 1 ,y = 2 , y 0 = - 1 and y 00 = - 32 9 . The linear approximation is 2.03, the quadratic
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This note was uploaded on 01/11/2011 for the course MATH MATH 140 taught by Professor Drury during the Fall '10 term at McGill.

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