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# Solutions for Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING

## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612

Solutions for Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING

Solutions for Chapter 4.4
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##### ISBN: 9780470888612

This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING includes 64 full step-by-step solutions. Calculus: Single and Multivariable was written by Patricia and is associated to the ISBN: 9780470888612. Since 64 problems in chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING have been answered, more than 13157 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
• Acute triangle

A triangle in which all angles measure less than 90°

• Bearing

Measure of the clockwise angle that the line of travel makes with due north

• Compounded continuously

Interest compounded using the formula A = Pert

• Compounded k times per year

Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

• Cube root

nth root, where n = 3 (see Principal nth root),

• Identity matrix

A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

• Initial value of a function

ƒ 0.

• Inverse of a matrix

The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

• Jump discontinuity at x a

limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• Logarithmic re-expression of data

Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

• Parameter interval

See Parametric equations.

• Period

See Periodic function.

• PH

The measure of acidity

• Range (in statistics)

The difference between the greatest and least values in a data set.

• Reflection across the x-axis

x, y and (x,-y) are reflections of each other across the x-axis.

• Residual

The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

• Scalar

A real number.

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

• Velocity

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

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