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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

Solutions for Chapter 1.1
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##### ISBN: 9780618149162

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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