L24 Math 233 Lecture Notes - Lecture 24: Lagrange Multiplier, Level Set, Nissan L Engine

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L24 Math 233 Lecture Notes - Lecture 23: Lagrange Multiplier, Nissan L Engine, Linear Independence

L24 Math 233 Lecture Notes - Lecture 24: Lagrange Multiplier, Level Set, Nissan L Engine

L24 Math 233 Lecture Notes - Lecture 25: Riemann Sum, Nissan L Engine, Iterated Integral

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L24 math 233 lecture 24- lagrange multipliers continued. Find the maximum/minimum of f(x,y) subject to the constraint g(x,y) = f by these steps: find x,y so that, solve for, check f(x,y) at all solutions f(x, ) in g(x,y) = k (cid:540) Note: this also works in 3d space with f(x,y,z) and g(x,y,z) = k. Find the points on the sphere away from (3,1,-1). x2 + y2 + z2 = 4 that are respectively, closest and farthest. Identify the constraint a. g (x, y z = x2 + y2 + z2 = 4. Identify f as the distance function a. f (x, y z = d ist((x, y z. Y z = < 2 3 2 1 2 + 1 > Y z = < 2 2 2 > , ) g(x, f(x, y z and collect terms. 1 (cid:540) y = 1: x = 3, solve for in the constraint equation- (cid:540) (1 (cid:540))2 + 12.

Related Questions

1. Use Lagrange multipliers to find the least distance between the point P(?3, 0, 4) and the surface of the cone z 2 = x 2 + y 2 .

2. Evaluate ? 2 0 ? 4 y 2 y sin(x 2 )dxdy.

3. Show that the volume V of the solid in the first octant bounded by the surface z = e y?x , the plane x + y = 1, and the coordinate planes satisfy V < cosh(1)

4. Set up the integral in spherical coordinates ? 1 0 ? ? 1?x2 0 ? ? 2?x2?y 2 ? x2+y 2 xydzdydx

5. Set up in polar coordinates the following double integral ? ? R ? x 2 + y 2dA; (R) bounded by x 2 + y 2 = 2x, y ? x, y ? 0.

6. Suppose a particle moving in space has velocity v(t) = ?sin(2t), cos(t), e?t ? and initial position x(0) = ?2, 1, 0?. Find the position vector function x(t).

7. : Find the maximum value of y x over (x ? 2)2 + y 2 .

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L24 Math 233 Lecture Notes - Lecture 24: Lagrange Multiplier, Level Set, Nissan L Engine

L24 Math 233 Lecture Notes - Lecture 23: Lagrange Multiplier, Nissan L Engine, Linear Independence

L24 Math 233 Lecture Notes - Lecture 24: Lagrange Multiplier, Level Set, Nissan L Engine

L24 Math 233 Lecture Notes - Lecture 25: Riemann Sum, Nissan L Engine, Iterated Integral

Document Summary

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