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Use the Divergence Theorem to find the outward flux of $\mathbf{F}$ across the boundary of the region $D$.Wedge $\quad \mathbf{F}=2 x z \mathbf{i}-x y \mathbf{j}-z^{2} \mathbf{k}$D: The wedge cut from the first octant by the plane $y+z=4$ and the elliptic cylinder $4 x^{2}+y^{2}=16$

$$-40 / 3$$

Calculus 1 / AB

Calculus 3

Chapter 15

Integrals and Vector Fields

Section 8

The Divergence Theorem and a Unified Theory

Integrals

Vectors

Vector Functions

Johns Hopkins University

Oregon State University

Harvey Mudd College

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

06:07

Use the Divergence Theorem…

03:09

In Exercises $5-16,$ use t…

12:53

17:47

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03:24

01:11

Use the divergence theorem…

people unequal 1/8 p. Two equal 1/4. This is some awful properties. It has to be equal one peacefully equal one minus 1/8 minus 1/4 equal five over eight. The smallest expected frequency is a product off the sample size and the smallest probability. P I equal m p one equal 15 times 1/8 equal 1.875 Equal MP on equal 16 times, 1/8 equal to equal MP, um equals 30 times. 1/8 equals 3.75 equals M P one equal 40 times 1/8 equal five equal M P. One equal 80 times, 1/8 equal 10. The conditions are met for the n. D. But de contains the smallest sample science.

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