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Unformatted text preview: (partial differentiation) Assume that all the given functions are differentiable. If ( 29 , u f x y = , where cos , sin s s x e t y e t = = , show that: (1) 2 2 2 2 2 s u u u u e x y s t ∂ ∂ ∂ ∂ + = + ÷ ÷ ÷ ÷ ∂ ∂ ∂ ∂ (2) 2 2 2 2 2 2 2 2 2 s u u u u e x y s t ∂ ∂ ∂ ∂ + = + ∂ ∂ ∂ ∂ . 2. If ( 29 z f x y = , show that z z x y ∂ ∂ + = ∂ ∂ . (conditional extreme) 1. Find the point on the plane 2 3 4 x y z + + = that is closest to the origin. (Answer: 2 4 6 , , 7 7 7 ÷ ) 2 ． A manufacturer produces a quantity Q of a certain product and Q depends on the amount x of labor used and the amount y of capital. A simple model that is sometimes used to express Q explicitly as a function of x and y is the CobbDouglas production function: 1 Q Ax y α α = , where A and α are constants with K and 0 1 α...
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This note was uploaded on 03/29/2012 for the course MATH 120 taught by Professor Folh during the Spring '08 term at Eastern Michigan University.
 Spring '08
 Folh
 Calculus, Addition

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