Single Variable Calculus: Early Transcendentals
8th Edition
ISBN: 9781305270336
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter H, Problem 14E
Evaluate the expression and write your answer in the form a + bi.
14.
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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 H Solutions
Single Variable Calculus: Early Transcendentals
Ch. H - Prob. 1ECh. H - Prob. 2ECh. H - Prob. 3ECh. H - Prob. 4ECh. H - Prob. 5ECh. H - Prob. 6ECh. H - Prob. 7ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 9ECh. H - Prob. 10E
Ch. H - Prob. 11ECh. H - Prob. 12ECh. H - Prob. 13ECh. H - Evaluate the expression and write your answer in...Ch. H - Prob. 15ECh. H - Prob. 16ECh. H - Prob. 17ECh. H - Prove the following properties of complex numbers....Ch. H - Prob. 19ECh. H - Prob. 20ECh. H - Prob. 21ECh. H - Find all solutions of the equation. 22. 2x2 2x +...Ch. H - Prob. 23ECh. H - Find all solutions of the equation. 24....Ch. H - Write the number in polar form with argument...Ch. H - Prob. 26ECh. H - Prob. 27ECh. H - Prob. 28ECh. H - Write the number in polar form with argument...Ch. H - Prob. 30ECh. H - Prob. 31ECh. H - Prob. 32ECh. H - Find the indicated power using De Moivres Theorem....Ch. H - Prob. 34ECh. H - Prob. 35ECh. H - Prob. 36ECh. H - Prob. 37ECh. H - Prob. 38ECh. H - Prob. 39ECh. H - Prob. 40ECh. H - Prob. 41ECh. H - Prob. 42ECh. H - Prob. 43ECh. H - Prob. 44ECh. H - Prob. 45ECh. H - Prob. 46ECh. H - Prob. 47ECh. H - Use Eulers formula to prove the following formulas...Ch. H - If u(x) = f(x) + ig(x) is a complex-valued...Ch. H - (a) If u is a complex-valued function of a real...
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- A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.arrow_forwardTopic 2 Evaluate S x dx, using u-substitution. Then find the integral using 1-x2 trigonometric substitution. Discuss the results! Topic 3 Explain what an elementary anti-derivative is. Then consider the following ex integrals: fed dx x 1 Sdx In x Joseph Liouville proved that the first integral does not have an elementary anti- derivative Use this fact to prove that the second integral does not have an elementary anti-derivative. (hint: use an appropriate u-substitution!)arrow_forward1. Given the vector field F(x, y, z) = -xi, verify the relation 1 V.F(0,0,0) = lim 0+ volume inside Se ff F• Nds SE where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then, determine if the origin is sink or source.arrow_forward
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- Question 8 Use the graph of f to evaluate the following: 6 f(x) 5 4 3 2 1 -1 1 2 3 4 5 -1 t The average rate of change of f from 4 to 5 = Question 9 10 ☑ 4parrow_forwardQuestion 15 ✓ 6 pts 1 Details The function shown below is f(x). We are interested in the transformed function g(x) = 3f(2x) - 1 a) Describe all the transformations g(x) has made to f(x) (shifts, stretches, etc). b) NEATLY sketch the transformed function g(x) and upload your graph as a PDF document below. You may use graph paper if you want. Be sure to label your vertical and horizontal scales so that I can tell how big your function is. 1- 0 2 3 4 -1- Choose File No file chosen Question 16 0 pts 1 Detailsarrow_forwardhelparrow_forward
- Question 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward1 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 .arrow_forwardanswerarrow_forward
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