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Solutions for Chapter 15: Multiple Integrals

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 15: Multiple Integrals

Solutions for Chapter 15
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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. Since 54 problems in chapter 15: Multiple Integrals have been answered, more than 53692 students have viewed full step-by-step solutions from this chapter. Chapter 15: Multiple Integrals includes 54 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12.

Key Calculus Terms and definitions covered in this textbook
  • 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)

  • Dot product

    The number found when the corresponding components of two vectors are multiplied and then summed

  • Equilibrium price

    See Equilibrium point.

  • Identity matrix

    A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

  • Index of summation

    See Summation notation.

  • Law of sines

    sin A a = sin B b = sin C c

  • Magnitude of a vector

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

  • Main diagonal

    The diagonal from the top left to the bottom right of a square matrix

  • Normal curve

    The graph of ƒ(x) = e-x2/2

  • Order of magnitude (of n)

    log n.

  • 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.

  • Pascal’s triangle

    A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

  • Positive angle

    Angle generated by a counterclockwise rotation.

  • Positive association

    A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

  • Standard form of a complex number

    a + bi, where a and b are real numbers

  • Standard form: equation of a circle

    (x - h)2 + (y - k2) = r 2

  • Synthetic division

    A procedure used to divide a polynomial by a linear factor, x - a

  • Vector

    An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

  • Vertical line

    x = a.

  • y-axis

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