#1

Reverse the order of integration and evaluate the integral.

G

X

dy dx

The reversed order of integration is

(Simplify your answers.)

The value of the integral is

(Type an exact answer.)

9 dydx

- (...

dx dy.

00

#2

Draw the solid region whose volume is given by the following double integral. Then find the volume of the solid.

is

01

Find the volume of the solid

V = 63

Draw the solid region whose volume is given by the double integral. Choose the correct graph below.

OA

(please solve the volume, 63 is the wrong answer)!

OC./n# 3

The function f(x,y) = 4x + 4y has an absolute maximum value and absolute minimum value subject to the

constraint 25x²2 - 25xy + 25y² = 1. Use Lagrange multipliers to find these values.

The absolute maximum value is 1.6 (Type an exact answer.)

The absolute minimum value is

(Type an exact answer.)

Please find the absolute minimum, absolute maximum is done!

#4

The function f(x,y) = 5xy has an absolute maximum value and absolute minimum value subject to the constraint

2x² + 2y²-3xy = 49. Use Lagrange multipliers to find these values.

The absolute maximum value is 245.

The absolute minimum value is

Please find the absolute minimum, absolute maximum is done!

# 5

The function f(x,y) = 5xy has an absolute maximum value and absolute minimum value subject to the

constraint x² + xy + y² = 36. Use Lagrange multipliers to find these values.

The absolute maximum is e

(Type an exact answer in terms of e.)

The absolute minimum is

(Type an exact answer in terms of e.)

Please find the absolute minimum, absolute maximum is done!/n#6

The function f(x,y,z) = 8x-3y + 6z has an absolute maximum value and absolute minimum value subject to the

constraint x² + y² + z² = 109. Use Lagrange multipliers to find these values.

2

The absolute maximum value is 109.

The absolute minimum value is

Please find the absolute minimum, absolute maximum is done!

C

#7

The function f(x,y,z) = 7x has an absolute maximum value and absolute minimum value subject to the constraint

-z-2. Use Lagrange multipliers to find these values.

x+1

The maximum value is 10.5.

The minimum value is

Please find the absolute minimum, absolute maximum is done!

# 8

The function f(x,y,z) = 6x+z² has an absolute maximum value and absolute minimum value subject to the

constraint 3x² + 2y² + 2z²=27. Use Lagrange multipliers to find these values.

The absolute maximum value is 19.5

The absolute minimum value is

Please find the absolute minimum, absolute maximum is done!