Solutions for Chapter 12: Vectors and the Geometry of 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 12: Vectors and the Geometry of Space

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

Since 76 problems in chapter 12: Vectors and the Geometry of Space have been answered, more than 3975 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. Chapter 12: Vectors and the Geometry of Space includes 76 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
  • Additive inverse of a complex number

    The opposite of a + bi, or -a - bi

  • Arccosecant function

    See Inverse cosecant function.

  • Binomial theorem

    A theorem that gives an expansion formula for (a + b)n

  • Bounded interval

    An interval that has finite length (does not extend to ? or -?)

  • Combination

    An arrangement of elements of a set, in which order is not important

  • First octant

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

  • Line of symmetry

    A line over which a graph is the mirror image of itself

  • Mathematical model

    A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

  • Midpoint (in Cartesian space)

    For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

  • Multiplication property of inequality

    If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

  • Natural logarithm

    A logarithm with base e.

  • Numerical derivative of ƒ at a

    NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002

  • Polynomial interpolation

    The process of fitting a polynomial of degree n to (n + 1) points.

  • Present value of an annuity T

    he net amount of your money put into an annuity.

  • Quadrantal angle

    An angle in standard position whose terminal side lies on an axis.

  • Rose curve

    A graph of a polar equation or r = a cos nu.

  • Row echelon form

    A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

  • Solution of an equation or inequality

    A value of the variable (or values of the variables) for which the equation or inequality is true

  • Sum of an infinite geometric series

    Sn = a 1 - r , |r| 6 1

  • x-axis

    Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

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