 15.3.1: If C is a piecewise smooth curve from (1, 2, 3) to (4, 5, 6),then C...
 15.3.2: If C is the portion of the circle x2 + y2 = 1 where 0 x,oriented co...
 15.3.3: A potential function for the vector fieldF(x, y, z) = yzi + (xz + z...
 15.3.4: If a, b, and c are nonzero real numbers such that the vectorfield x...
 15.3.5: 16 Determine whether F is a conservative vector field. If so,find a...
 15.3.6: 16 Determine whether F is a conservative vector field. If so,find a...
 15.3.7: In each part, evaluate C 2xy3 dx + (1 + 3x2y2) dy overthe curve C, ...
 15.3.8: (a) Show that the line integral C y sin x dx cos x dy isindependent...
 15.3.9: 914 Show that the integral is independent of the path, and useTheor...
 15.3.10: 914 Show that the integral is independent of the path, and useTheor...
 15.3.11: 914 Show that the integral is independent of the path, and useTheor...
 15.3.12: 914 Show that the integral is independent of the path, and useTheor...
 15.3.13: 914 Show that the integral is independent of the path, and useTheor...
 15.3.14: 914 Show that the integral is independent of the path, and useTheor...
 15.3.15: 1518 Confirm that the force field F is conservative in someopen con...
 15.3.16: 1518 Confirm that the force field F is conservative in someopen con...
 15.3.17: 1518 Confirm that the force field F is conservative in someopen con...
 15.3.18: 1518 Confirm that the force field F is conservative in someopen con...
 15.3.19: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.3.20: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.3.21: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.3.22: 1922 TrueFalse Determine whether the statement is true orfalse. Exp...
 15.3.23: 2324 Find the exact value of C F dr using any method. F(x, y) = (ey...
 15.3.24: 2324 Find the exact value of C F dr using any method. F(x, y) = 2xy...
 15.3.25: Use the numerical integration capability of a CAS or othercalculati...
 15.3.26: Use the numerical integration capability of a CAS or othercalculati...
 15.3.27: 2728 Is the vector field conservative? Explain. 27
 15.3.28: 2728 Is the vector field conservative? Explain. 28
 15.3.29: Suppose thatC is a circle in the domain of a conservativenonzero ve...
 15.3.30: Does the result in Exercise 29 remain true if the circleC is replac...
 15.3.31: Prove: IfF(x, y, z) = f(x, y, z)i + g(x, y, z)j + h(x, y, z)kis a c...
 15.3.32: Use the result in Exercise 31 to show that the integralCyz dx + xz ...
 15.3.33: Find a nonzero function h for whichF(x, y) = h(x)[x sin y + y cos y...
 15.3.34: (a) In Example 3 of Section 15.1 we showed that(x, y) = c(x2 + y2)1...
 15.3.35: 3536 Use the result in Exercise 34(b). In each part, find the work ...
 15.3.36: 3536 Use the result in Exercise 34(b). Let F(x, y) = yx2 + y2 i xx2...
 15.3.37: Prove Theorem 15.3.1 if C is a piecewise smooth curvecomposed of sm...
 15.3.38: Prove that (b) implies (c) in Theorem 15.3.2. [Hint: Considerany tw...
 15.3.39: Complete the proof of Theorem 15.3.2 by showing that/y = g(x, y), w...
 15.3.40: Writing Describe the different methods available for evaluatingthe ...
 15.3.41: Writing Discuss some of the ways that you can show avector field is...
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
Get Full SolutionsThis 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 stepbystep solutions from this chapter. Chapter 15.3: INDEPENDENCE OF PATH; CONSERVATIVE VECTOR FIELDS includes 41 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10.

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 xaxis

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 zaxis in a graph.

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

Onetoone 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