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# Solutions for Chapter 1.2: Mathematical Induction

## Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 1.2: Mathematical Induction

Solutions for Chapter 1.2
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##### ISBN: 9780471321484

Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 1.2: Mathematical Induction includes 20 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Since 20 problems in chapter 1.2: Mathematical Induction have been answered, more than 6967 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Angular speed

Speed of rotation, typically measured in radians or revolutions per unit time

• 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

• Circle graph

A circular graphical display of categorical data

• Common ratio

See Geometric sequence.

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Hyperbola

A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

• Interquartile range

The difference between the third quartile and the first quartile.

• Jump discontinuity at x a

limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

• Length of a vector

See Magnitude of a vector.

• Numerical derivative of ƒ at a

NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002

• Parabola

The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

• 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.

• Range (in statistics)

The difference between the greatest and least values in a data set.

• Rational function

Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

• Solve a triangle

To find one or more unknown sides or angles of a triangle

• Spiral of Archimedes

The graph of the polar curve.

• Standard unit vectors

In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

• Tangent

The function y = tan x

• xy-plane

The points x, y, 0 in Cartesian space.

• Yscl

The scale of the tick marks on the y-axis in a viewing window.

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