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Solutions for Chapter 13: Vector-Valued Functions and Motion in Space

Thomas' Calculus | 12th Edition | ISBN: 9780321587992 | Authors: George B. Thomas Jr.

Full solutions for Thomas' Calculus | 12th Edition

ISBN: 9780321587992

Thomas' Calculus | 12th Edition | ISBN: 9780321587992 | Authors: George B. Thomas Jr.

Solutions for Chapter 13: Vector-Valued Functions and Motion in Space

Solutions for Chapter 13
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Textbook: Thomas' Calculus
Edition: 12
Author: George B. Thomas Jr.
ISBN: 9780321587992

Thomas' Calculus was written by and is associated to the ISBN: 9780321587992. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13: Vector-Valued Functions and Motion in Space includes 32 full step-by-step solutions. Since 32 problems in chapter 13: Vector-Valued Functions and Motion in Space have been answered, more than 10641 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12.

Key Calculus Terms and definitions covered in this textbook
  • Absolute value of a complex number

    The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

  • Deductive reasoning

    The process of utilizing general information to prove a specific hypothesis

  • Differentiable at x = a

    ƒ'(a) exists

  • Irrational zeros

    Zeros of a function that are irrational numbers.

  • Line graph

    A graph of data in which consecutive data points are connected by line segments

  • Line of travel

    The path along which an object travels

  • Magnitude of a vector

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

  • Natural logarithm

    A logarithm with base e.

  • Open interval

    An interval that does not include its endpoints.

  • Parallelogram representation of vector addition

    Geometric representation of vector addition using the parallelogram determined by the position vectors.

  • Parametric equations for a line in space

    The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

  • Product of a scalar and a vector

    The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

  • Series

    A finite or infinite sum of terms.

  • 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.

  • Venn diagram

    A visualization of the relationships among events within a sample space.

  • Vertex of a cone

    See Right circular cone.

  • Vertical translation

    A shift of a graph up or down.

  • Weighted mean

    A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

  • Ymax

    The y-value of the top of the viewing window.

  • Ymin

    The y-value of the bottom of the viewing window.

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