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Solutions for Chapter 6.1: The Derivative

Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 6.1: The Derivative

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 17 problems in chapter 6.1: The Derivative have been answered, more than 8784 students have viewed full step-by-step solutions from this chapter. Chapter 6.1: The Derivative includes 17 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
  • Binomial coefficients

    The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!

  • Branches

    The two separate curves that make up a hyperbola

  • Constant term

    See Polynomial function

  • Degree

    Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

  • Graph of a polar equation

    The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

  • Inverse tangent function

    The function y = tan-1 x

  • Leading coefficient

    See Polynomial function in x

  • Multiplication property of equality

    If u = v and w = z, then uw = vz

  • nth root

    See Principal nth root

  • Ordered pair

    A pair of real numbers (x, y), p. 12.

  • Plane in Cartesian space

    The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

  • Radicand

    See Radical.

  • 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.

  • Solve graphically

    Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

  • Speed

    The magnitude of the velocity vector, given by distance/time.

  • Symmetric about the y-axis

    A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is

  • Synthetic division

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

  • Transitive property

    If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

  • Trigonometric form of a complex number

    r(cos ? + i sin ?)

  • Unit ratio

    See Conversion factor.

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