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Solutions for Chapter 1.1: A Preview of Calculus

Full solutions for Calculus of A Single Variable | 7th Edition

ISBN: 9780618149162

Solutions for Chapter 1.1: A Preview of Calculus

This textbook survival guide was created for the textbook: Calculus of A Single Variable, edition: 7. Calculus of A Single Variable was written by and is associated to the ISBN: 9780618149162. Chapter 1.1: A Preview of Calculus includes 11 full step-by-step solutions. Since 11 problems in chapter 1.1: A Preview of Calculus have been answered, more than 23737 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Key Calculus Terms and definitions covered in this textbook
  • Absolute maximum

    A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

  • Absolute value of a real number

    Denoted by |a|, represents the number a or the positive number -a if a < 0.

  • Algebraic model

    An equation that relates variable quantities associated with phenomena being studied

  • Characteristic polynomial of a square matrix A

    det(xIn - A), where A is an n x n matrix

  • Extracting square roots

    A method for solving equations in the form x 2 = k.

  • Frequency (in statistics)

    The number of individuals or observations with a certain characteristic.

  • Graph of a function ƒ

    The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

  • Implicitly defined function

    A function that is a subset of a relation defined by an equation in x and y.

  • Logarithmic form

    An equation written with logarithms instead of exponents

  • Mathematical induction

    A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

  • Mathematical model

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

  • Matrix element

    Any of the real numbers in a matrix

  • Parabola

    The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

  • 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.

  • Power function

    A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

  • Response variable

    A variable that is affected by an explanatory variable.

  • Rigid transformation

    A transformation that leaves the basic shape of a graph unchanged.

  • Scatter plot

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

  • Semiminor axis

    The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

  • Upper bound for real zeros

    A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

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