Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 4.4, Problem 2TF
To determine
To find: The function f has given derivative
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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 4 Solutions
Calculus
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Prob. 26SCh. 4.5 - Prob. 27SCh. 4.5 - Prob. 28SCh. 4.5 - Prob. 29SCh. 4.5 - Prob. 30SCh. 4.5 - Prob. 31SCh. 4.5 - Prob. 32SCh. 4.5 - Prob. 33SCh. 4.5 - Prob. 34SCh. 4.5 - Prob. 35SCh. 4.5 - Prob. 36SCh. 4.5 - Prob. 37SCh. 4.5 - Prob. 38SCh. 4.5 - Prob. 39SCh. 4.5 - Prob. 40SCh. 4.5 - Prob. 41SCh. 4.5 - Prob. 42SCh. 4.5 - Prob. 43SCh. 4.5 - Prob. 44SCh. 4.5 - Prob. 45SCh. 4.5 - Prob. 46SCh. 4.5 - Prob. 47SCh. 4.5 - Prob. 48SCh. 4.5 - Prob. 49SCh. 4.5 - Prob. 50SCh. 4.5 - Prob. 51SCh. 4.5 - Prob. 52SCh. 4.5 - Prob. 53SCh. 4.5 - Prob. 54SCh. 4.5 - Prob. 55SCh. 4.5 - Prob. 56SCh. 4.5 - Prob. 57SCh. 4.5 - Prob. 58SCh. 4.5 - Prob. 59SCh. 4.5 - Prob. 60SCh. 4.5 - Prob. 61SCh. 4.5 - Prob. 62SCh. 4.5 - Prob. 63SCh. 4.5 - Prob. 64SCh. 4.5 - Prob. 65ACh. 4.5 - Prob. 66ACh. 4.5 - Prob. 67ACh. 4.5 - Prob. 68ACh. 4.5 - Prob. 69ACh. 4.5 - Prob. 70ACh. 4.5 - Prob. 71ACh. 4.5 - Prob. 72PCh. 4.5 - Prob. 73PCh. 4.5 - Prob. 74PCh. 4.5 - Prob. 75PCh. 4.5 - Prob. 76PCh. 4.5 - Prob. 77PCh. 4.5 - Prob. 78PCh. 4.5 - 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- 4 3 2 -5 4-3 -2 -1 1 2 3 4 5 12 23 -4 The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)arrow_forwardQuestion 4 The plot below represents the function f(x) 8 7 3 pts O -4-3-2-1 6 5 4 3 2 + 1 2 3 5 -2+ Evaluate f(3) f(3) = Solve f(x) = 3 x= Question 5arrow_forwardQuestion 14 6+ 5 4 3 2 -8-2 2 3 4 5 6 + 2 3 4 -5 -6 The graph above is a transformation of the function f(x) = |x| Write an equation for the function graphed above g(x) =arrow_forward
- 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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