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Solutions for Chapter 3: The Derivative

Calculus:Early Transcendentals | 7th Edition | ISBN: 9780131569898 | Authors: C. Henry Edwards

Full solutions for Calculus:Early Transcendentals | 7th Edition

ISBN: 9780131569898

Calculus:Early Transcendentals | 7th Edition | ISBN: 9780131569898 | Authors: C. Henry Edwards

Solutions for Chapter 3: The Derivative

Solutions for Chapter 3
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Textbook: Calculus:Early Transcendentals
Edition: 7
Author: C. Henry Edwards
ISBN: 9780131569898

Summary of Chapter 3: The Derivative

The definition of the derivative. The rate of change of a function with respect to a variable. Operator notation for derivatives.

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: The Derivative includes 125 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 125 problems in chapter 3: The Derivative have been answered, more than 40233 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
  • Arrow

    The notation PQ denoting the directed line segment with initial point P and terminal point Q.

  • Back-to-back stemplot

    A stemplot with leaves on either side used to compare two distributions.

  • Base

    See Exponential function, Logarithmic function, nth power of a.

  • Definite integral

    The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

  • Exponential growth function

    Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

  • Focus, foci

    See Ellipse, Hyperbola, Parabola.

  • Graph of a relation

    The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

  • Imaginary part of a complex number

    See Complex number.

  • Inverse composition rule

    The composition of a one-toone function with its inverse results in the identity function.

  • Jump discontinuity at x a

    limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

  • Length of a vector

    See Magnitude of a vector.

  • Mean (of a set of data)

    The sum of all the data divided by the total number of items

  • Number line graph of a linear inequality

    The graph of the solutions of a linear inequality (in x) on a number line

  • Phase shift

    See Sinusoid.

  • Polynomial in x

    An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

  • Radian measure

    The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

  • Scatter plot

    A plot of all the ordered pairs of a two-variable data set on a coordinate plane.

  • Tangent line of ƒ at x = a

    The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

  • Unbounded interval

    An interval that extends to -? or ? (or both).

  • Zero factor property

    If ab = 0 , then either a = 0 or b = 0.