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# Solutions for Chapter 5.1: Areas and Distances ## Full solutions for Calculus, | 5th Edition

ISBN: 9780534393397 Solutions for Chapter 5.1: Areas and Distances

Solutions for Chapter 5.1
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##### ISBN: 9780534393397

This textbook survival guide was created for the textbook: Calculus,, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.1: Areas and Distances includes 26 full step-by-step solutions. Calculus, was written by and is associated to the ISBN: 9780534393397. Since 26 problems in chapter 5.1: Areas and Distances have been answered, more than 47399 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Average velocity

The change in position divided by the change in time.

• Bounded below

A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

• Coefficient

The real number multiplied by the variable(s) in a polynomial term

• Cube root

nth root, where n = 3 (see Principal nth root),

• Damping factor

The factor Ae-a in an equation such as y = Ae-at cos bt

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Horizontal Line Test

A test for determining whether the inverse of a relation is a function.

• Independent variable

Variable representing the domain value of a function (usually x).

• Left-hand limit of f at x a

The limit of ƒ as x approaches a from the left.

• Limit at infinity

limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

• Linear inequality in two variables x and y

An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

• Lower bound for real zeros

A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

• Origin

The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space

• Orthogonal vectors

Two vectors u and v with u x v = 0.

• Square matrix

A matrix whose number of rows equals the number of columns.

• Statistic

A number that measures a quantitative variable for a sample from a population.

• Terminal side of an angle

See Angle.

• Tree diagram

A visualization of the Multiplication Principle of Probability.

• Unbounded interval

An interval that extends to -? or ? (or both).

• Unit vector

Vector of length 1.

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