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# Solutions for Chapter 3: Calculus:Early Transcendentals 7th Edition ## Full solutions for Calculus:Early Transcendentals | 7th Edition

ISBN: 9780131569898 Solutions for Chapter 3

Solutions for Chapter 3
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##### ISBN: 9780131569898

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3 includes 125 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 125 problems in chapter 3 have been answered, more than 9298 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Common ratio

See Geometric sequence.

• Composition of functions

(f ? g) (x) = f (g(x))

• Equivalent systems of equations

Systems of equations that have the same solution.

• Fitting a line or curve to data

Finding a line or curve that comes close to passing through all the points in a scatter plot.

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Identity function

The function ƒ(x) = x.

• Implicitly defined function

A function that is a subset of a relation defined by an equation in x and y.

• Independent variable

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

• Linear function

A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

• LRAM

A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval

• Main diagonal

The diagonal from the top left to the bottom right of a square matrix

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• Ordered pair

A pair of real numbers (x, y), p. 12.

• Periodic function

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

• Positive angle

Angle generated by a counterclockwise rotation.

• 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

• Sphere

A set of points in Cartesian space equally distant from a fixed point called the center.

• Upper bound for ƒ

Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

• Variance

The square of the standard deviation.

• Vertex of a parabola

The point of intersection of a parabola and its line of symmetry.

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