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exercises4 - 1(a gradf =(3-7 gradf(17 39 =(3-7 1(b gradf...

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Gradient and directional derivative 1. Find the grad f and the grad f ( P ). (a) f ( x, y ) = 3 x - 7 y , P (17 , 39) (b) f ( x, y ) = 3 x 2 - 5 y 2 , P (2 , - 3) (c) f ( x, y ) = e - x 2 - y 2 , P (0 , 0) 2. Find the directional derivative of f at P in the direction of -→ v . (a) f ( x, y ) = x 2 + 2 xy + 3 y 2 , P (2 , 1), -→ v = (1 , 1) (b) f ( x, y ) = x 3 - x 2 y + xy 2 + y 3 , P (1 , - 1), -→ v = (2 , 3) (c) f ( x, y ) = sin x cos y , P ( π/ 3 , - 2 π/ 3), -→ v = (4
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Unformatted text preview: 1(a) gradf = (3 ,-7), gradf (17 , 39) = (3 ,-7) 1(b) gradf = (6 x,-10 y ), gradf (2 ,-3) = (12 , 30) 1(c) gradf = (-2 xe-x 2-y 2 ,-2 ye-x 2-y 2 ), gradf (0 , 0) = (0 , 0) 2(a) 8 √ 2 2(b) 12 √ 13 13 2(c)-13 10...
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