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# Solutions for Chapter 12.1: Thomas' Calculus: Early Transcendentals 13th Edition

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

ISBN: 9780321884077

Solutions for Chapter 12.1

Solutions for Chapter 12.1
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##### ISBN: 9780321884077

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. Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. Chapter 12.1 includes 66 full step-by-step solutions. Since 66 problems in chapter 12.1 have been answered, more than 27104 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• artesian coordinate system

An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers

• Cosine

The function y = cos x

• Determinant

A number that is associated with a square matrix

• Distance (in a coordinate plane)

The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1 - x 2)2 + (y1 - y2)2

• Focal length of a parabola

The directed distance from the vertex to the focus.

• Frequency distribution

See Frequency table.

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Independent events

Events A and B such that P(A and B) = P(A)P(B)

• Index of summation

See Summation notation.

• Minor axis

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

• Parametrization

A set of parametric equations for a curve.

• Placebo

In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

• Probability function

A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

An equation that can be written in the form ax 2 + bx + c = 01a ? 02

• Reciprocal of a real number

See Multiplicative inverse of a real number.

• Recursively defined sequence

A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

• Remainder polynomial

See Division algorithm for polynomials.

• Rose curve

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

• Semimajor axis

The distance from the center to a vertex of an ellipse.

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

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