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# Solutions for Chapter 4.1: Limits of Functions

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

ISBN: 9780471321484

Solutions for Chapter 4.1: Limits of Functions

Solutions for Chapter 4.1
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##### ISBN: 9780471321484

This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.1: Limits of Functions includes 16 full step-by-step solutions. Since 16 problems in chapter 4.1: Limits of Functions have been answered, more than 2632 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

If u = v and w = z , then u + w = v + z

• Causation

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

• Difference of complex numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

• Direct variation

See Power function.

• Direction of an arrow

The angle the arrow makes with the positive x-axis

• Endpoint of an interval

A real number that represents one “end” of an interval.

• Fundamental

Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

• Identity

An equation that is always true throughout its domain.

• Instantaneous rate of change

See Derivative at x = a.

• Instantaneous velocity

The instantaneous rate of change of a position function with respect to time, p. 737.

• Length of a vector

See Magnitude of a vector.

• Mode of a data set

The category or number that occurs most frequently in the set.

• Natural logarithm

A logarithm with base e.

• Odd function

A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

• Outliers

Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

• Product of a scalar and a vector

The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

• Right angle

A 90° angle.

• Standard form: equation of a circle

(x - h)2 + (y - k2) = r 2

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• Ymin

The y-value of the bottom of the viewing window.

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