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# Solutions for Chapter 4.2: Area ## Full solutions for Calculus | 9th Edition

ISBN: 9780547167022 Solutions for Chapter 4.2: Area

Solutions for Chapter 4.2
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##### ISBN: 9780547167022

This expansive textbook survival guide covers the following chapters and their solutions. Since 93 problems in chapter 4.2: Area have been answered, more than 17995 students have viewed full step-by-step solutions from this chapter. Calculus was written by Patricia and is associated to the ISBN: 9780547167022. This textbook survival guide was created for the textbook: Calculus , edition: 9. Chapter 4.2: Area includes 93 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Absolute value of a vector

See Magnitude of a vector.

• 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.

• Characteristic polynomial of a square matrix A

det(xIn - A), where A is an n x n matrix

• Complex fraction

See Compound fraction.

• Definite integral

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

• Directed angle

See Polar coordinates.

• Direction angle of a vector

The angle that the vector makes with the positive x-axis

• Equivalent systems of equations

Systems of equations that have the same solution.

• Exponential form

An equation written with exponents instead of logarithms.

• Future value of an annuity

The net amount of money returned from an annuity.

• kth term of a sequence

The kth expression in the sequence

• Magnitude of a real number

See Absolute value of a real number

• Normal curve

The graph of ƒ(x) = e-x2/2

• Orthogonal vectors

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

• Quantitative variable

A variable (in statistics) that takes on numerical values for a characteristic being measured.

• Removable discontinuity at x = a

lim x:a- ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

• Rose curve

A graph of a polar equation or r = a cos nu.

• Sine

The function y = sin x.

• Vector equation for a line in space

The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

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