14.7-15.2

14.7-15.2 - x 2 1 x 2 2 ·· x 2 n = 1 4 Calculate the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 231 Group Work Quiz Related 1. Find the absolute maximum and minimum values of he function f on the set D . (a) f ( x,y ) = 3 + xy - x - y 2 , where D is the triangle bounded by the points (0 , 0), (2 , 0), (1 , 1). (b) f ( x,y ) = 4 x + 6 y - x 2 - y 2 , where D = { ( x,y ) | 0 x 3 , | y | ≤ 1 } . (c) f ( x,y ) = 7 - x 2 y , where D = { ( x,y ) | x 0 ,y 0 ,x 2 + y 2 3 } . 2. Find the volume of the solid enclosed by the surface z = e x sin y and the planes x = ± 1, y = 0, y = π , z = - 1. 3. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (a) f ( x,y,z ) = ( xyz ) 2 , where x 2 + y 2 + z 2 = 1. (b) f ( x,y,z ) = x 2 + y 2 + z 2 , where x 4 + y 4 + z 4 = 1. (c) f ( x 1 ,x 2 ,...,x n ) = x 1 + x 2 + ··· + x n , where
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x 2 1 + x 2 2 + ··· + x 2 n = 1. 4. Calculate the double integral. (a) ZZ R 1 + x 2 1 + y 2 dA, R = [0 , 1] × [0 , 1] (b) ZZ R x x 2 + y 2 dA, R = [1 , 2] × [0 , 1] (c) ZZ R cos x + sin y dA, R = [0 ,π ] × [0 ,π/ 2] 5. Find the average value of f ( x,y ) = e y √ x + e y over the rectangle [0 , 4] × [0 , 1]. 6. Find the maximum and minimum volumes of a rectangular box whose surface area is 1000 cm 3 and whose total edge length is 200 cm. 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online