sn9_1 - -19.84 b) -12.32 c) -16.16 d) -11.36 e) 11.68 15.9...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 2433 – Week 9 Popper 009 1. Find the point(s) on the surface at which the tangent plane is horizontal. a) b) c) d) e) 2. What is today? a) Tuesday b) Wednesday c) Thursday 15.7 - Maxima and Minima with Side Conditions Examples: 1. Maximize xy on the ellipse 2 2 4 9 36 x y + = .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
2. Minimize 2 4 x y z + + on the sphere 2 2 2 7 x y z + + = . 3. Find the points on the sphere 2 2 2 1 x y z + + = that are closest to and farthest from the point (3, 1, 3).
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Hint for #20: 15.8 – Differentials Recall from Calc I: Now, for ( , ) f x y , the differential ( ) df f x h = ∇ h h i or And for ( , , ) f x y z
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Examples: 1. Find the differential df a. b.
Background image of page 6
2. 3. Use differentials to approximate 4 125 17
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Popper009 3. Find the differential df . a) b) c) d) e) 4. Use differentials to approximate the value of f at the point P . a)
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -19.84 b) -12.32 c) -16.16 d) -11.36 e) 11.68 15.9 - Reconstructing a Function from its Gradient The gradient of a function ( , ) f x y is ( , ) f x y = So if we have a (gradient) vector in the form ( , ) P x y i + ( , ) Q x y j We can begin reconstruct the function by setting P = / f x and Q = / f y Now when integrating / f x with respect to x , remember that y is a constant! Example: xy 2 i + x 2 y j Note: Sometimes the given vector could not be the gradient of a function. More examples: Popper009 5. Determine whether or not the vector function is the gradient f ( x , y ) of a function everywhere defined. If so, find all the functions with that gradient. a) b) c) d) e) 6. D...
View Full Document

This note was uploaded on 07/20/2010 for the course MATH 18427 taught by Professor Etgen during the Fall '10 term at University of Houston.

Page1 / 11

sn9_1 - -19.84 b) -12.32 c) -16.16 d) -11.36 e) 11.68 15.9...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online