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# Solutions for Chapter 5.3: Continuous Functions on Intervals

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

ISBN: 9780471321484

Solutions for Chapter 5.3: Continuous Functions on Intervals

Solutions for Chapter 5.3
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##### ISBN: 9780471321484

Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. 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. Chapter 5.3: Continuous Functions on Intervals includes 19 full step-by-step solutions. Since 19 problems in chapter 5.3: Continuous Functions on Intervals have been answered, more than 6953 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Ambiguous case

The case in which two sides and a nonincluded angle can determine two different triangles

• Average rate of change of ƒ over [a, b]

The number ƒ(b) - ƒ(a) b - a, provided a ? b.

• Average velocity

The change in position divided by the change in time.

• Center

The central point in a circle, ellipse, hyperbola, or sphere

• Completing the square

A method of adding a constant to an expression in order to form a perfect square

• Compounded annually

See Compounded k times per year.

• Constant function (on an interval)

ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

• Difference of two vectors

<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>

• Directed line segment

See Arrow.

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• 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.

• Implied domain

The domain of a function’s algebraic expression.

• Inequality

A statement that compares two quantities using an inequality symbol

• Natural numbers

The numbers 1, 2, 3, . . . ,.

• Ordered pair

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

• Pascal’s triangle

A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

• Polar form of a complex number

See Trigonometric form of a complex number.

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

• Regression model

An equation found by regression and which can be used to predict unknown values.

• Venn diagram

A visualization of the relationships among events within a sample space.

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