 12.1.1E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.2E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.3E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.4E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.5E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.6E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.7E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.8E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.9E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.10E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.11E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.12E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.13E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.14E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.15E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.16E: Geometric Interpretations of EquationsIn Exercise, give a geometric...
 12.1.17E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.18E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.19E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.20E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.21E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.22E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.23E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.24E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.25E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.26E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.27E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.28E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.29E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.30E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.31E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.32E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.33E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.34E: Geometric Interpretations of Inequalities and EquationsIn Exercise,...
 12.1.35E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.36E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.37E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.38E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.39E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.40E: Inequalities to Describe Sets of PointsWrite inequalities to descri...
 12.1.41E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.42E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.43E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.44E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.45E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.46E: DistanceIn Exercise, find the distance between points P1 and P2.P 1...
 12.1.47E: Spheres Find the centers and radii of the spheres in Exercise.
 12.1.48E: SpheresFind the centers and radii of the spheres in Exercise.()2 + ...
 12.1.49E: SpheresFind the centers and radii of the spheres in Exercise.2 + 2 ...
 12.1.50E: SpheresFind the centers and radii of the spheres in Exercise.2 + 2 ...
 12.1.51E: SpheresFind equations for the spheres whose centers and radii are g...
 12.1.52E: SpheresFind equations for the spheres whose centers and radii are g...
 12.1.53E: SpheresFind equations for the spheres whose centers and radii are g...
 12.1.54E: SpheresFind equations for the spheres whose centers and radii are g...
 12.1.55E: SpheresFind the centers and radii of the spheres in Exercise.
 12.1.56E: SpheresFind the centers and radii of the spheres in Exercise.
 12.1.57E: SpheresFind the centers and radii of the spheres in Exercise.
 12.1.58E: SpheresFind the centers and radii of the spheres in Exercise.
 12.1.59E: Theory and ExamplesFind a formula for the distance from the point P...
 12.1.60E: Theory and ExamplesFind a formula for the distance from the point P...
 12.1.61E: Theory and ExamplesFind the perimeter of the triangle with vertices...
 12.1.62E: Theory and ExamplesShow that the point P(3, 1, 2) is equidistant fr...
 12.1.63E: Theory and ExamplesFind an equation for the set of all points equid...
 12.1.64E: Theory and ExamplesFind an equation for the set of all points equid...
 12.1.65E: Theory and ExamplesFind the point on the sphere 2 + ()2 + ()2 = 4 n...
 12.1.66E: Theory and ExamplesFind the point equidistant from the points (0, 0...
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
Get Full SolutionsThis textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. This expansive textbook survival guide covers the following chapters and their solutions. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. Chapter 12.1 includes 66 full stepbystep solutions. Since 66 problems in chapter 12.1 have been answered, more than 217370 students have viewed full stepbystep solutions from this chapter.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Closed interval
An interval that includes its endpoints

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

Distance (on a number line)
The distance between real numbers a and b, or a  b

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Focal length of a parabola
The directed distance from the vertex to the focus.

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Leading coefficient
See Polynomial function in x

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Proportional
See Power function

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

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

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

Standard deviation
A measure of how a data set is spread

Stemplot (or stemandleaf plot)
An arrangement of a numerical data set into a specific tabular format.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.