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# Solutions for Chapter 12.2: Thomas' Calculus: Early Transcendentals 13th Edition

## Full solutions for Thomas' Calculus: Early Transcendentals | 13th Edition

ISBN: 9780321884077

Solutions for Chapter 12.2

Solutions for Chapter 12.2
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##### ISBN: 9780321884077

This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Chapter 12.2 includes 56 full step-by-step solutions. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 12.2 have been answered, more than 83723 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Component form of a vector

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

• Confounding variable

A third variable that affects either of two variables being studied, making inferences about causation unreliable

• Control

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

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Deductive reasoning

The process of utilizing general information to prove a specific hypothesis

• Derivative of ƒ

The function defined by ƒ'(x) = limh:0ƒ(x + h) - ƒ(x)h for all of x where the limit exists

• Equivalent systems of equations

Systems of equations that have the same solution.

• Geometric series

A series whose terms form a geometric sequence.

• Implied domain

The domain of a function’s algebraic expression.

• Inverse tangent function

The function y = tan-1 x

• Irrational zeros

Zeros of a function that are irrational numbers.

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• Multiplication property of inequality

If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

• Negative numbers

Real numbers shown to the left of the origin on a number line.

• Octants

The eight regions of space determined by the coordinate planes.

• Parallel lines

Two lines that are both vertical or have equal slopes.

• Perpendicular lines

Two lines that are at right angles to each other

• Reference angle

See Reference triangle

• Solve algebraically

Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

• Vertical translation

A shift of a graph up or down.

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