 Lv 2718 points

# ?

• ### Estimating volume of the solid that lies above the square and below the elliptic paraboloid?

The square is: R=[0,8] x [0,8]

the elliptic paraboloid: f(x,y) = 65 - 4x^2 - 3y^2

Divide R into four equal squares and use the Midpoint Rule.

• ### Find relative extrema of f on the region described by the inequality?

f(x,y) = 5e^(xy)

5x^2 + 3y^2 =< 1

• ### Find relative extrema of f on the region described by the inequality?

f(x,y) = 5e^(xy)

5x^2 + 3y^2 =< 1

• ### Lagrange Multipliers for maximum?

f(x,y,z) = 13x^4 + 13y^4 +13z^4

g(x,y,z) = 13x^2 + 13y^2 + 13z^2 = 4

a) 16/13

b) 12/13

c) 8/13

d) 48/169

I know that ∇F = λ∇G

where ∇F = < 52x^3, 52y^3, 52z^3 > and ∇G = < 26x, 26y, 26z >

therefore:

x = y = z = √λ/2

But when I plug this into the constraint and solve for λ, I get √4/39, and when I plug this into f(x,y,z) I get 16/39 :(

• ### Use Lagrange multipliers to the maximum value of the function subject to the given constraint?

f(x,y,z) = 5xyz

constraint: g(x,y,z) = 5x^2 +20y^2 +20z - 21 = 0

I know that ∇F = λ∇G

where ∇F = < 5yz, 5xz, 5xy > and ∇G = < 10x, 40y, 20 >

which would give me:

5yz = 10x λ and 5xz = 40yλ and 5xy = 20λ

but I'm having trouble with solving for x, y, and z

• ### Use Lagrange multipliers to find the maximum value of the function subject to the given constraint?

f(x,y) = 3x^2 - 8y^2

constraint: 3x^2 + 8y^2 = 5

I have the gradientF as < 6x, -16y > and the gradientG = < 6x, 16y >

but...I don't know what to do now...

• ### HELP! Identify this organic compound?

The compound only contains C, H, and O. It's a liquid with a boiling point of 206 degrees Celsius and has a molecular weight of 138. It also only contains one kind of functional group.