Calculus3_test2_formulasheet-1

# Calculus3_test2_formulasheet-1 - f j =-r r r Normal Line y...

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14.2 Surfaces 14.3 Graph level curves 2 2 ( , ) 1,0,1,2 f x y x y c c x y = - = - = - { } 2 2 2 2 2 2 2 2 ( , ) ( , ) : 4 9 Int: 4 9 Bnd: 4, 9 f x y x y x y x y x y x y = + < + < + = + = { } 2 ( , ) ( , ):1 4 1 Int: 1 1, 2 2 2 Bnd: 1, 2 f x y x y x x x x x x x = = - < < - < < = = = { } ( , ) ( , ):2 4, 1 y 3 Int: 2 4, 1 3 Bnd: union of the 4 line segments that bnd the rectangle. f x y x y x x y = < < < < 14.6 Limits 15.2 Directional Derivative ( ) u f f x u x = g 15.3 Mean Value Thereom ( ) ( ) ( ) ( ) f b f a f c b a - = - g Chain Rule [ ] ( ( )) ( ( )) ( ) d f r t f r t r t dt x = g 15.4 Normal Vector: x y f f i f j = + r r Tangent Line: 0 0 ( ) ( ) 0 x y f x x f y y - + - = Tangent Vector: y x t f i

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Unformatted text preview: f j =-r r r Normal Line: ( ) ( ) y x f x x f y y---= Tangent Plane: ( ) ( ) ( ) x y z f x x f y y f z z-+-+-= Normal Line: x x x f t = + y y y f t = + z z z f t = + 15.5 A B C xx xy yy f f f = = = 2 D AC B =-D>0 then D<0 saddle pt. A>0 local min A<0 local max 15.8 Differentials ( , , ) ( , , ) x y z df f x f y f z df f f f x x y y z z f x y z = + + = + + +-V V V V V V V V...
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Calculus3_test2_formulasheet-1 - f j =-r r r Normal Line y...

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