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# Solutions for Chapter 3.5: The Cauchy Criterion

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

ISBN: 9780471321484

Solutions for Chapter 3.5: The Cauchy Criterion

Solutions for Chapter 3.5
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##### ISBN: 9780471321484

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Chapter 3.5: The Cauchy Criterion includes 14 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 14 problems in chapter 3.5: The Cauchy Criterion have been answered, more than 9701 students have viewed full step-by-step solutions from this chapter. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484.

Key Calculus Terms and definitions covered in this textbook
• Causation

A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

• Complex number

An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

• Conditional probability

The probability of an event A given that an event B has already occurred

• Continuous at x = a

lim x:a x a ƒ(x) = ƒ(a)

• Division algorithm for polynomials

Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

• Frequency

Reciprocal of the period of a sinusoid.

• Leibniz notation

The notation dy/dx for the derivative of ƒ.

• Mapping

A function viewed as a mapping of the elements of the domain onto the elements of the range

• Measure of an angle

The number of degrees or radians in an angle

• Midpoint (on a number line)

For the line segment with endpoints a and b, a + b2

• Octants

The eight regions of space determined by the coordinate planes.

• Perihelion

The closest point to the Sun in a planet’s orbit.

• Projection of u onto v

The vector projv u = au # vƒvƒb2v

• Reference angle

See Reference triangle

• Remainder polynomial

See Division algorithm for polynomials.

• 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>

• Translation

See Horizontal translation, Vertical translation.

• Unit vector

Vector of length 1.

• Velocity

A vector that specifies the motion of an object in terms of its speed and direction.

• Vertex of a parabola

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

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