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# Solutions for Chapter 4.1: Differentials and Taylors Theorem

## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652

Solutions for Chapter 4.1: Differentials and Taylors Theorem

Solutions for Chapter 4.1
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##### ISBN: 9780321780652

Vector Calculus was written by and is associated to the ISBN: 9780321780652. This expansive textbook survival guide covers the following chapters and their solutions. Since 43 problems in chapter 4.1: Differentials and Taylors Theorem have been answered, more than 13532 students have viewed full step-by-step solutions from this chapter. Chapter 4.1: Differentials and Taylors Theorem includes 43 full step-by-step solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4.

Key Calculus Terms and definitions covered in this textbook
• Average velocity

The change in position divided by the change in time.

• Bearing

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

• Compound interest

Interest that becomes part of the investment

• Damping factor

The factor Ae-a in an equation such as y = Ae-at cos bt

• Dependent variable

Variable representing the range value of a function (usually y)

• First-degree equation in x , y, and z

An equation that can be written in the form.

• Identity

An equation that is always true throughout its domain.

• Logarithm

An expression of the form logb x (see Logarithmic function)

• Magnitude of a vector

The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

• nth root of a complex number z

A complex number v such that vn = z

• Piecewise-defined function

A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

• Polar distance formula

The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22

• Product of matrices A and B

The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

• Recursively defined sequence

A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

• Right circular cone

The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

• Scatter plot

A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

A graph in which (-x, -y) is on the the graph whenever (x, y) is; or a graph in which (-r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

• Transitive property

If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

• Vertices of a hyperbola

The points where a hyperbola intersects the line containing its foci.

• z-axis

Usually the third dimension in Cartesian space.

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