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Solutions for Chapter 3: Vector-Valued Functions

Vector Calculus | 4th Edition | ISBN: 9780321780652 | Authors: Susan J. Colley

Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652

Vector Calculus | 4th Edition | ISBN: 9780321780652 | Authors: Susan J. Colley

Solutions for Chapter 3: Vector-Valued Functions

Solutions for Chapter 3
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Textbook: Vector Calculus
Edition: 4
Author: Susan J. Colley
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.

  • Quadratic equation in x

    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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