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# Solutions for Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2

## Full solutions for Calculus: Single Variable | 6th Edition

ISBN: 9780470888643

Solutions for Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2

Solutions for Chapter 5.4
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##### ISBN: 9780470888643

This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2 includes 79 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 79 problems in chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2 have been answered, more than 34790 students have viewed full step-by-step solutions from this chapter. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643.

Key Calculus Terms and definitions covered in this textbook
• Average rate of change of ƒ over [a, b]

The number ƒ(b) - ƒ(a) b - a, provided a ? b.

• Circular functions

Trigonometric functions when applied to real numbers are circular functions

• Constraints

See Linear programming problem.

• 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

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• Derivative of ƒ

The function defined by ƒ'(x) = limh:0ƒ(x + h) - ƒ(x)h for all of x where the limit exists

• Division

a b = aa 1 b b, b Z 0

• Equivalent equations (inequalities)

Equations (inequalities) that have the same solutions.

• Gaussian elimination

A method of solving a system of n linear equations in n unknowns.

• Jump discontinuity at x a

limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

• Multiplicity

The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x - c) (x - z 2) Á (x - z n)

• Octants

The eight regions of space determined by the coordinate planes.

• Ordered set

A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

• Range screen

See Viewing window.

• Reflection

Two points that are symmetric with respect to a lineor a point.

• Slant asymptote

An end behavior asymptote that is a slant line

• Solution of an equation or inequality

A value of the variable (or values of the variables) for which the equation or inequality is true

• Standard form: equation of a circle

(x - h)2 + (y - k2) = r 2

• Stem

The initial digit or digits of a number in a stemplot.

• 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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