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# Solutions for Chapter 11: The Calculus of Variable-Factor Products

## Full solutions for Calculus: Concepts and Applications | 2nd Edition

ISBN: 9781559536547

Solutions for Chapter 11: The Calculus of Variable-Factor Products

Solutions for Chapter 11
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##### ISBN: 9781559536547

Chapter 11: The Calculus of Variable-Factor Products includes 9 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Concepts and Applications was written by and is associated to the ISBN: 9781559536547. Since 9 problems in chapter 11: The Calculus of Variable-Factor Products have been answered, more than 18590 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Concepts and Applications, edition: 2.

Key Calculus Terms and definitions covered in this textbook
• Algebraic model

An equation that relates variable quantities associated with phenomena being studied

• Angle

Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

• Component form of a vector

If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)

• Convenience sample

A sample that sacrifices randomness for convenience

• Coordinate plane

See Cartesian coordinate system.

• Derivative of ƒ at x a

ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists

• Difference identity

An identity involving a trigonometric function of u - v

• Fitting a line or curve to data

Finding a line or curve that comes close to passing through all the points in a scatter plot.

• 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.

• Horizontal component

See Component form of a vector.

• Hyperbola

A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

• Identity properties

a + 0 = a, a ? 1 = a

• kth term of a sequence

The kth expression in the sequence

• Main diagonal

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

• Matrix, m x n

A rectangular array of m rows and n columns of real numbers

• Multiplicative inverse of a matrix

See Inverse of a matrix

• Origin

The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space

• Random numbers

Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

• Reflection across the y-axis

x, y and (-x,y) are reflections of each other across the y-axis.

• y-coordinate

The directed distance from the x-axis xz-plane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.

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