# Solutions for Chapter 14.6: Thomas' Calculus: Early Transcendentals 13th Edition

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

ISBN: 9780321884077

Solutions for Chapter 14.6

Solutions for Chapter 14.6
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##### ISBN: 9780321884077

Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. Since 58 problems in chapter 14.6 have been answered, more than 35176 students have viewed full step-by-step solutions from this chapter. Chapter 14.6 includes 58 full step-by-step solutions. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Complex fraction

See Compound fraction.

• Dihedral angle

An angle formed by two intersecting planes,

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Dot product

The number found when the corresponding components of two vectors are multiplied and then summed

• Exponential decay function

Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

• Infinite discontinuity at x = a

limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.

• Intermediate Value Theorem

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

• Inverse function

The inverse relation of a one-to-one function.

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Logarithm

An expression of the form logb x (see Logarithmic function)

• Magnitude of a vector

The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

• Nonsingular matrix

A square matrix with nonzero determinant

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

• Random variable

A function that assigns real-number values to the outcomes in a sample space.

• Remainder polynomial

See Division algorithm for polynomials.

• Solve by elimination or substitution

Methods for solving systems of linear equations.

• 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>.

• Vertical translation

A shift of a graph up or down.

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