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# Solutions for Chapter 5.2: Combinations of Continuous Functions

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

ISBN: 9780471321484

Solutions for Chapter 5.2: Combinations of Continuous Functions

Solutions for Chapter 5.2
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##### ISBN: 9780471321484

This expansive textbook survival guide covers the following chapters and their solutions. Since 15 problems in chapter 5.2: Combinations of Continuous Functions have been answered, more than 8093 students have viewed full step-by-step solutions from this chapter. Chapter 5.2: Combinations of Continuous Functions includes 15 full step-by-step 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.

Key Calculus Terms and definitions covered in this textbook

P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

• 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

• Common logarithm

A logarithm with base 10.

• Expanded form

The right side of u(v + w) = uv + uw.

• Horizontal line

y = b.

• Integers

The numbers . . ., -3, -2, -1, 0,1,2,...2

• Inverse tangent function

The function y = tan-1 x

• Lemniscate

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

• Matrix element

Any of the real numbers in a matrix

• Multiplicative inverse of a real number

The reciprocal of b, or 1/b, b Z 0

• NDER ƒ(a)

See Numerical derivative of ƒ at x = a.

• Opens upward or downward

A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

• Partial sums

See Sequence of partial sums.

• Period

See Periodic function.

• Polynomial interpolation

The process of fitting a polynomial of degree n to (n + 1) points.

A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

• Rational zeros

Zeros of a function that are rational numbers.

• Remainder polynomial

See Division algorithm for polynomials.

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• System

A set of equations or inequalities.

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