MATH 221 MNSU Calculus III Quiz III I have to do math homework. The class is calculus III……………………………… Math 221 Summer, 2020 Name: J

MATH 221 MNSU Calculus III Quiz III I have to do math homework. The class is calculus III……………………………… Math 221
Summer, 2020
Name:
July 19, 2020
Quiz 3 (14.8, 15.1, 15.2, 15.3, 15.5, 15.6)
1. This extreme value problem has a solution with both a maximum value and
a minimum value. Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.
f (x, y, z) = 4x + 4y + 5z;
1
2×2 + 2y 2 + 5z 2 = 21
2. Calculate the iterated integral.
!
1
0
!
y
0
(2x +
2
y2
1
) dx dy
+1
3. Evaluate the integral by reversing the order of integration.
!
2
0
!
6
3y
3
2
ex dx dy
4. Evaluate the integral by converting to polar coordinates.
!
2
−2
!
√
0
4−x2
sin(x2 + y 2 ) dy dx
4
5. Find the volume of the solid under of the plane z = x and above the region
D in the first quadrant that lies between the circles x2 +y 2 = 1 and x2 +y 2 = 9.
5
6.
! ! !
E
yz cos(3×5 ) dV, where E = {(x, y, z)|0 ≤ x ≤ 1, 0 ≤ y ≤ x, x ≤ z ≤ 2x}
6

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