2. Use Lagrange Multipliers to find the points on the surface z² = 16+xy that are closest to the origin. a. (±4, 0, 0) b. (0, 0, ±16) c. (0, 0, ±4) d. (1, 1, ±2) e. (2, 2, ±1) Evaluate the double integral by first identifying it as the volume of a solid. (15-2x) dd, R = {(x, y)|4≤x≤ 8, 4 ≤y ≤7} R a. -64 b. 36 c. -164 d. 236 e. 136 Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 7-6x²-6y² and the plane z = 1. . 4.5 T обл . . З п 13 л 2π
2. Use Lagrange Multipliers to find the points on the surface z² = 16+xy that are closest to the origin. a. (±4, 0, 0) b. (0, 0, ±16) c. (0, 0, ±4) d. (1, 1, ±2) e. (2, 2, ±1) Evaluate the double integral by first identifying it as the volume of a solid. (15-2x) dd, R = {(x, y)|4≤x≤ 8, 4 ≤y ≤7} R a. -64 b. 36 c. -164 d. 236 e. 136 Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 7-6x²-6y² and the plane z = 1. . 4.5 T обл . . З п 13 л 2π
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You only have to do #32 and 34
Transcribed Image Text:r
32. Use Lagrange Multipliers to find the points on the surface z² = 16+xy that are closest to the origin.
a. (±4, 0, 0)
b. (0, 0, ± 16)
c. (0, 0, ±4)
d. (1, 1, ±2)
e. (2, 2, ±1)
33. Evaluate the double integral by first identifying it as the volume of a solid.
(15-2x) d4, R = {(x, y)|4 ≤x≤8, 4≤ y ≤7}
a. -64
b. 36
c. -164
d. 236
e. 136
34. Use polar coordinates to find the volume of the solid bounded by the paraboloid z=7-6x²-6y² and the
plane z = 1.
a. 4.5 π
b. 6 π
с. 13 п
d. 3 π
е. 2π
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