Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
Author: James Stewart
Publisher: Cengage Learning
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Chapter B, Problem 19E
To determine
To write: The sum
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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 B Solutions
Essential Calculus: Early Transcendentals
Ch. B - Prob. 1ECh. B - Write the sum in expanded form. 2. i=161i+1Ch. B - Write the sum in expanded form. 3. i=463iCh. B - Write the sum in expanded form. 4. i=46i3Ch. B - Write the sum in expanded form. 5. k=042k12k+1Ch. B - Write the sum in expanded form. 6. k=58xkCh. B - Write the sum in expanded form. 7. i=1ni10Ch. B - Write the sum in expanded form. 8. j=nn+3j2Ch. B - Write the sum in expanded form. 9. j=0n1(1)jCh. B - Write the sum in expanded form. 10. i=1nf(xi)xi
Ch. B - Write the sum in sigma notation. 11. 1 + 2 + 3 + 4...Ch. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Write the sum in sigma notation. 20. 1 x + x2 x3...Ch. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Find the value of the sum. 30. i=1n(25i)Ch. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Find the value of the sum. 35. i=1n(i3i2)Ch. B - Find the number n such that i=1ni=78.Ch. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prove the generalized triangle inequality:...Ch. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50E
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