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# Solutions for Chapter 3: Vector-Valued Functions ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 3: Vector-Valued Functions

Solutions for Chapter 3
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##### ISBN: 9780321780652

This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Chapter 3: Vector-Valued Functions includes 44 full step-by-step solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Since 44 problems in chapter 3: Vector-Valued Functions have been answered, more than 12457 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°

• Annuity

A sequence of equal periodic payments.

• Components of a vector

See Component form of a vector.

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Demand curve

p = g(x), where x represents demand and p represents price

• Exponential form

An equation written with exponents instead of logarithms.

• First octant

The points (x, y, z) in space with x > 0 y > 0, and z > 0.

• Geometric sequence

A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

• Initial side of an angle

See Angle.

• Inverse cosine function

The function y = cos-1 x

• Law of sines

sin A a = sin B b = sin C c

• Logarithmic re-expression of data

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

• 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.

An equation that can be written in the form ax 2 + bx + c = 01a ? 02

• Shrink of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.

• Sum of a finite arithmetic series

Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,

• Transpose of a matrix

The matrix AT obtained by interchanging the rows and columns of A.

• Vertices of an ellipse

The points where the ellipse intersects its focal axis.

• y-axis

Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

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