additional exercises - (partial differentiation Assume that...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 Cobb-Douglas production function: 1 Q Ax y α α- = , where A and α are constants with K and 0 1 α...
View Full Document

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.

Page1 / 3

additional exercises - (partial differentiation Assume that...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online