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# Solutions for Chapter 6: Line Integrals ## Full solutions for Vector Calculus | 4th Edition

ISBN: 9780321780652 Solutions for Chapter 6: Line Integrals

Solutions for Chapter 6
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##### ISBN: 9780321780652

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 6: Line Integrals includes 39 full step-by-step solutions. Since 39 problems in chapter 6: Line Integrals have been answered, more than 12652 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Compound fraction

A fractional expression in which the numerator or denominator may contain fractions

• Conditional probability

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

• 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

• Distance (in a coordinate plane)

The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1 - x 2)2 + (y1 - y2)2

• DMS measure

The measure of an angle in degrees, minutes, and seconds

• Equivalent arrows

Arrows that have the same magnitude and direction.

• Five-number summary

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

• Future value of an annuity

The net amount of money returned from an annuity.

• Geometric sequence

A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

• Jump discontinuity at x a

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

• kth term of a sequence

The kth expression in the sequence

• Limit at infinity

limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

• Local maximum

A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

• Probability of an event in a finite sample space of equally likely outcomes

The number of outcomes in the event divided by the number of outcomes in the sample space.

• Randomization

The principle of experimental design that makes it possible to use the laws of probability when making inferences.

• Reciprocal identity

An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

• Reflection through the origin

x, y and (-x,-y) are reflections of each other through the origin.

• Standard form: equation of a circle

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

• Symmetric property of equality

If a = b, then b = a

• Vertices of an ellipse

The points where the ellipse intersects its focal axis.

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