 20.1.1: Is curl(zi xj + yk ) a vector or a scalar? Calculate it.
 20.1.2: Is curl(2zi zj +xyk ) a vector or scalar? Calculateit.
 20.1.3: In Exercises 310, compute the curl of the vector field.F = 3xi 5zj ...
 20.1.4: In Exercises 310, compute the curl of the vector field.F = (x2 y2)i...
 20.1.5: In Exercises 310, compute the curl of the vector field.F = (x + y)i...
 20.1.6: In Exercises 310, compute the curl of the vector field.F = 2yzi + 3...
 20.1.7: In Exercises 310, compute the curl of the vector field.F = x2i + y3...
 20.1.8: In Exercises 310, compute the curl of the vector field.F = exi + co...
 20.1.9: In Exercises 310, compute the curl of the vector field.F = (x + yz)...
 20.1.10: In Exercises 310, compute the curl of the vector field.F (r ) = r /r
 20.1.11: In Exercises 1114, decide whether the vector field appears tohave n...
 20.1.12: In Exercises 1114, decide whether the vector field appears tohave n...
 20.1.13: In Exercises 1114, decide whether the vector field appears tohave n...
 20.1.14: In Exercises 1114, decide whether the vector field appears tohave n...
 20.1.15: Let F be the vector field in Figure 20.2 on page 1048.It is rotatin...
 20.1.16: Use the geometric definition to find the curl of the vectorfield F ...
 20.1.17: A smooth vector field G has curl G (0, 0, 0) = 2i 3j + 5k . Estimat...
 20.1.18: Three small circles, C1, C2, and C3, each with radius0.1 and center...
 20.1.19: Using your answers to Exercises 78, make a conjectureabout a partic...
 20.1.20: (a) Find curl G if G = (ay3+bez)i + (cz +dx2)j +(e sin x + f y)k an...
 20.1.21: Figure 20.9 gives a sketch of the velocity vector fieldF = yi + xj ...
 20.1.22: A tornado is formed when a tube of air circling a horizontalaxis is...
 20.1.23: A large fire becomes a firestorm when the nearby air acquiresa cir...
 20.1.24: A vortex that rotates at constant angular velocity aboutthe zaxis ...
 20.1.25: A central vector field is one of the form F = f(r)rwhere f is any f...
 20.1.26: Show that curl (F + C ) = curl F for a constant vectorfield C .
 20.1.27: If F is any vector field whose components have continuoussecond par...
 20.1.28: We have seen that the Fundamental Theorem of Calculusfor Line Integ...
 20.1.29: Show that curl (F ) = curl F + (grad ) F for ascalar function and a...
 20.1.30: . Show that if F = f grad g for some scalar functions fand g, then ...
 20.1.31: Let F be a smooth vector field and let u and v be constantvectors. ...
 20.1.32: Let T = ai + bj be a fixed unit vector, and letF = F(x, y)T be a ve...
 20.1.33: Let r = (x2+y2)1/2. Figure 20.10 shows the vector fieldrA(yi + xj )...
 20.1.34: In 3435, explain what is wrong with the statement.A vector field F ...
 20.1.35: In 3435, explain what is wrong with the statement.If all the vector...
 20.1.36: In 3637, give an example of:A vector field F (x, y, z) such that cu...
 20.1.37: In 3637, give an example of:A vector field F (x, y, z) such that cu...
 20.1.38: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.39: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.40: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.41: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.42: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.43: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.44: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.45: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.46: In 3846, is the statement true or false? Assume Fand G are smooth v...
 20.1.47: Of the following vector fields, which ones have a curlwhich is para...
Solutions for Chapter 20.1: THE CURL OF A VECTOR FIELD
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 20.1: THE CURL OF A VECTOR FIELD
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 20.1: THE CURL OF A VECTOR FIELD includes 47 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 47 problems in chapter 20.1: THE CURL OF A VECTOR FIELD have been answered, more than 43661 students have viewed full stepbystep solutions from this chapter.

Arccotangent function
See Inverse cotangent function.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Direct variation
See Power function.

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

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

Imaginary part of a complex number
See Complex number.

Implied domain
The domain of a function’s algebraic expression.

Limit to growth
See Logistic growth function.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

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

Phase shift
See Sinusoid.

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

Reflexive property of equality
a = a

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Sum of a finite geometric series
Sn = a111  r n 2 1  r

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.

Ymax
The yvalue of the top of the viewing window.