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# Solutions for Chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS

## Full solutions for Calculus: Early Transcendentals, | 10th Edition

ISBN: 9780470647691

Solutions for Chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS

Solutions for Chapter 15.3
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##### ISBN: 9780470647691

This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Since 41 problems in chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS have been answered, more than 40231 students have viewed full step-by-step solutions from this chapter. Chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS includes 41 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a vector

See Magnitude of a vector.

• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Direction of an arrow

The angle the arrow makes with the positive x-axis

• 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

• Equally likely outcomes

Outcomes of an experiment that have the same probability of occurring.

• Feasible points

Points that satisfy the constraints in a linear programming problem.

• First quartile

See Quartile.

• Frequency distribution

See Frequency table.

• Function

A relation that associates each value in the domain with exactly one value in the range.

• Heron’s formula

The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.

• Increasing on an interval

A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

• Intercept

Point where a curve crosses the x-, y-, or z-axis in a graph.

• Interval

Connected subset of the real number line with at least two points, p. 4.

• One-to-one rule of exponents

x = y if and only if bx = by.

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

• 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).

• Right triangle

A triangle with a 90° angle.

• Simple harmonic motion

Motion described by d = a sin wt or d = a cos wt

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Symmetric difference quotient of ƒ at a

ƒ(x + h) - ƒ(x - h) 2h

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