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# Solutions for Chapter 16: Integration in Vector Fields

## Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992

Solutions for Chapter 16: Integration in Vector Fields

Solutions for Chapter 16
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##### ISBN: 9780321587992

This expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 16: Integration in Vector Fields have been answered, more than 11551 students have viewed full step-by-step solutions from this chapter. Thomas' Calculus was written by and is associated to the ISBN: 9780321587992. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Chapter 16: Integration in Vector Fields includes 60 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Additive inverse of a real number

The opposite of b , or -b

• Control

The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

• Data

Facts collected for statistical purposes (singular form is datum)

• Deductive reasoning

The process of utilizing general information to prove a specific hypothesis

• Frequency distribution

See Frequency table.

• Geometric sequence

A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

• Intermediate Value Theorem

If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

• Law of cosines

a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• LRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval

• Power regression

A procedure for fitting a curve y = a . x b to a set of data.

• Probability simulation

A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

• Regression model

An equation found by regression and which can be used to predict unknown values.

• Row operations

See Elementary row operations.

• Sine

The function y = sin x.

• Standard deviation

A measure of how a data set is spread

• Sum of functions

(ƒ + g)(x) = ƒ(x) + g(x)

• Symmetric difference quotient of ƒ at a

ƒ(x + h) - ƒ(x - h) 2h

• Zero vector

The vector <0,0> or <0,0,0>.

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