THOMAS' CALC. EARLY TRANS.W/ACCESS
14th Edition
ISBN: 9780135430903
Author: Hass
Publisher: PEARSON
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Chapter 13, Problem 3AAE
To determine
Verify that
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3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 13 Solutions
THOMAS' CALC. EARLY TRANS.W/ACCESS
Ch. 13.1 - In Exercises 1–4, find the given limits.
1.
Ch. 13.1 - In Exercises 1–4, find the given limits.
2.
Ch. 13.1 - In Exercises 1–4, find the given limits.
3.
Ch. 13.1 - In Exercises 1–4, find the given limits.
4.
Ch. 13.1 - Motion in the Plane
In Exercises 5–8, r(t) is the...Ch. 13.1 - Motion in the Plane
In Exercises 5–8, r(t) is the...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - In Exercises 19–22, r(t) is the position of a...Ch. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - Tangents to Curves
As mentioned in the text, the...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - Prob. 29ECh. 13.1 - In Exercises 27-30, find the value(s) of t so that...Ch. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 37ECh. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - Prob. 42ECh. 13.1 - Prob. 43ECh. 13.1 - Prob. 44ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.2 - Evaluate the integrals in Exercises 1–10.
1.
Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Evaluate the integrals in Exercises 1–10.
4.
Ch. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Evaluate the integrals in Exercises 1–10.
8.
Ch. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Prob. 13ECh. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Solve the initial value problems in Exercises...Ch. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - Throwing a baseball A baseball is thrown from the...Ch. 13.2 - Prob. 27ECh. 13.2 - Beaming electrons An electron in a TV tube is...Ch. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 -
Launching downhill An ideal projectile is...Ch. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Prob. 41ECh. 13.2 - Hitting a baseball with linear drag Consider the...Ch. 13.2 - Prob. 43ECh. 13.2 - Prob. 44ECh. 13.2 - Prob. 45ECh. 13.2 - Prob. 46ECh. 13.2 -
Hitting a baseball with linear drag under a wind...Ch. 13.2 - Prob. 48ECh. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - In Exercises 1–8, find the curve’s unit tangent...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - In Exercises 11–14, find the arc length parameter...Ch. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Length of helix The length of the turn of the...Ch. 13.3 - Length is independent of parametrization To...Ch. 13.3 - Prob. 19ECh. 13.3 - (Continuation of Exercise 19.) Find the unit...Ch. 13.3 - Distance along a line Show that if u is a unit...Ch. 13.3 - Prob. 22ECh. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - Prob. 3ECh. 13.4 - Find T, N, and κ for the plane curves in Exercises...Ch. 13.4 - A formula for the curvature of the graph of a...Ch. 13.4 - A formula for the curvature of a parametrized...Ch. 13.4 -
Normals to plane curves
Show that n(t) = −g′(t)i...Ch. 13.4 - (Continuation of Exercise 7.)
Use the method of...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Prob. 12ECh. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Find T, N, and κ for the space curves in Exercises...Ch. 13.4 - Show that the parabola , has its largest curvature...Ch. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Find an equation for the circle of curvature of...Ch. 13.4 - Find an equation for the circle of curvature of...Ch. 13.4 - Prob. 23ECh. 13.4 - The formula
derived in Exercise 5, expresses the...Ch. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Osculating circle Show that the center of the...Ch. 13.4 - Prob. 30ECh. 13.5 - In Exercises 1 and 2, write a in the form a = aTT...Ch. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - In Exercises 7 and 8, find r, T, N, and B at the...Ch. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Prob. 25ECh. 13.5 - Prob. 26ECh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - Prob. 4ECh. 13.6 - Prob. 5ECh. 13.6 - In Exercises 1–7, find the velocity and...Ch. 13.6 - Prob. 7ECh. 13.6 - Type of orbit For what values of v0 in Equation...Ch. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13 - Prob. 1GYRCh. 13 - Prob. 2GYRCh. 13 - Prob. 3GYRCh. 13 - Prob. 4GYRCh. 13 - Prob. 5GYRCh. 13 - Prob. 6GYRCh. 13 - Prob. 7GYRCh. 13 - Prob. 8GYRCh. 13 - Prob. 9GYRCh. 13 - Prob. 10GYRCh. 13 - Prob. 11GYRCh. 13 - Prob. 12GYRCh. 13 - Prob. 13GYRCh. 13 - Prob. 1PECh. 13 - Prob. 2PECh. 13 - Prob. 3PECh. 13 - Prob. 4PECh. 13 - Prob. 5PECh. 13 - Prob. 6PECh. 13 - Prob. 7PECh. 13 - Prob. 8PECh. 13 - Prob. 9PECh. 13 - Prob. 10PECh. 13 - Prob. 11PECh. 13 - Prob. 12PECh. 13 - Prob. 13PECh. 13 - Prob. 14PECh. 13 - Prob. 15PECh. 13 - Prob. 16PECh. 13 - Prob. 17PECh. 13 - Prob. 18PECh. 13 - Prob. 19PECh. 13 - Prob. 20PECh. 13 - Prob. 21PECh. 13 - Prob. 22PECh. 13 - Prob. 23PECh. 13 - Prob. 24PECh. 13 - Prob. 25PECh. 13 - Prob. 26PECh. 13 - Prob. 27PECh. 13 - Prob. 28PECh. 13 - Prob. 29PECh. 13 - Prob. 30PECh. 13 - Prob. 31PECh. 13 - Prob. 32PECh. 13 - Prob. 1AAECh. 13 - Prob. 2AAECh. 13 - Prob. 3AAECh. 13 - Prob. 4AAECh. 13 - Prob. 5AAECh. 13 - Prob. 6AAECh. 13 - Prob. 7AAECh. 13 - Prob. 8AAECh. 13 - Prob. 9AAE
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