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# Solutions for Chapter 4: Calculus of a Single Variable 8th Edition ## Full solutions for Calculus of a Single Variable | 8th Edition

ISBN: 9780618503032 Solutions for Chapter 4

Solutions for Chapter 4
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##### ISBN: 9780618503032

This textbook survival guide was created for the textbook: Calculus of a Single Variable, edition: 8. Chapter 4 includes 20 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus of a Single Variable was written by and is associated to the ISBN: 9780618503032. Since 20 problems in chapter 4 have been answered, more than 1788 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook

If u = v and w = z , then u + w = v + z

• Binomial theorem

A theorem that gives an expansion formula for (a + b)n

• Conditional probability

The probability of an event A given that an event B has already occurred

• Cycloid

The graph of the parametric equations

• Differentiable at x = a

ƒ'(a) exists

• Distributive property

a(b + c) = ab + ac and related properties

• First quartile

See Quartile.

• Five-number summary

The minimum, first quartile, median, third quartile, and maximum of a data set.

• Integrable over [a, b] Lba

ƒ1x2 dx exists.

• Inverse relation (of the relation R)

A relation that consists of all ordered pairs b, a for which a, b belongs to R.

• Negative association

A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

• Odd-even identity

For a basic trigonometric function f, an identity relating f(x) to f(-x).

• Periodic function

A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

• Plane in Cartesian space

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

• Polar equation

An equation in r and ?.

A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

• Quartile

The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

• Standard representation of a vector

A representative arrow with its initial point at the origin

• Vector equation for a line in space

The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

• Work

The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.

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