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Solutions for Chapter 11.3: Continuous Functions

Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 11.3: Continuous Functions

Solutions for Chapter 11.3
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ISBN: 9780471321484

Since 10 problems in chapter 11.3: Continuous Functions have been answered, more than 2595 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 11.3: Continuous Functions includes 10 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Absolute maximum

A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

• Coordinate plane

See Cartesian coordinate system.

• Cotangent

The function y = cot x

• Course

See Bearing.

• Distance (on a number line)

The distance between real numbers a and b, or |a - b|

• Dot product

The number found when the corresponding components of two vectors are multiplied and then summed

• Eccentricity

A nonnegative number that specifies how off-center the focus of a conic is

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Instantaneous rate of change

See Derivative at x = a.

• Inverse variation

See Power function.

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Linear programming problem

A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

• Lower bound for real zeros

A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

• Multiplicative inverse of a matrix

See Inverse of a matrix

• Probability of an event in a finite sample space of equally likely outcomes

The number of outcomes in the event divided by the number of outcomes in the sample space.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

• Real part of a complex number

See Complex number.

• Vertex of a cone

See Right circular cone.

• xy-plane

The points x, y, 0 in Cartesian space.

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