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# Solutions for Chapter 4: INTEGRALS ## Full solutions for Essential Calculus (Available Titles CengageNOW) | 1st Edition

ISBN: 9780495014423 Solutions for Chapter 4: INTEGRALS

Solutions for Chapter 4
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##### ISBN: 9780495014423

This expansive textbook survival guide covers the following chapters and their solutions. Essential Calculus (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780495014423. Chapter 4: INTEGRALS includes 261 full step-by-step solutions. This textbook survival guide was created for the textbook: Essential Calculus (Available Titles CengageNOW), edition: 1. Since 261 problems in chapter 4: INTEGRALS have been answered, more than 16483 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Angular speed

Speed of rotation, typically measured in radians or revolutions per unit time

• Associative properties

a + (b + c) = (a + b) + c, a(bc) = (ab)c.

• Coordinate(s) of a point

The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space

• Cube root

nth root, where n = 3 (see Principal nth root),

• Equivalent arrows

Arrows that have the same magnitude and direction.

• Equivalent systems of equations

Systems of equations that have the same solution.

• Five-number summary

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

• Half-plane

The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Lower bound test for real zeros

A test for finding a lower bound for the real zeros of a polynomial

• Multiplication property of equality

If u = v and w = z, then uw = vz

• Negative linear correlation

See Linear correlation.

• Opens upward or downward

A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

• Positive angle

Angle generated by a counterclockwise rotation.

• Rectangular coordinate system

See Cartesian coordinate system.

• Speed

The magnitude of the velocity vector, given by distance/time.

• Stretch of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.

• Sum identity

An identity involving a trigonometric function of u + v

• Sum of a finite geometric series

Sn = a111 - r n 2 1 - r

• Unit vector in the direction of a vector

A unit vector that has the same direction as the given vector.

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