Quiz_2_20C_Solution

Quiz_2_20C_Solution - Math 20C (Shenk). Quiz 2 Solution....

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Math 20C (Shenk). Quiz 2 Solution. August 23, 2010. 1. y = e 2 x y = 2 e 2 x y ′′ = 4 e 2 x y (0) = 2 y ′′ (0) = 4 κ (0) = y ′′ (0) { 1 + [ y (0)] 2 } 3 / 2 = 4 (1 + 2 2 ) 3 / 2 = 4 5 3 / 2 2. v = < 3 , 4 > [Speed] = | v | = 3 2 + 4 2 = 5 T = v | v | = < 3 5 , 4 5 > N = < 4 5 , 3 5 > d 2 s dt 2 = 5 κ = 2 a = d 2 s dt 2 T + κ p ds dt P 2 N = 5 < 3 5 , 4 5 > +( 2)(5 2 ) < 4 5 , 3 5 > = < 3 , 4 > < 40 , 30 > = < 43 , 26 > feet per second 2 3 (a) From the level curve L = 3 to the level curve L = 2 along y = 10: Δ L = 2 3 = 1 and Δ x 5 L x (20 , 10) Δ L Δ x 1 5 = 0 . 2 (b) From the level curve L = 2 to the level curve L = 3 on the line through (20 , 10) and the origin, Δ L = 3 2 = 1 and Δ s 4. [Directional derivative ] Δ L Δ s 1 4 = 0 . 25 4. M x = M (6 , 1) M (1 , 1) 6 1 = 30 20 5 = 4 M y = M
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Quiz_2_20C_Solution - Math 20C (Shenk). Quiz 2 Solution....

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