Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 50SP
To determine
To find:Thegiven line integral.
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Students have asked these similar questions
Incorrect.
Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the
vector field v = y² i +1.1x² j using 5 steps with At = 0.1.
Find the exact values of x1, ... , x5 and y1, ... , y5 and then fill in the blanks rounding your numbers to
three decimal places.
X1 =
!Yı =
i
X2
i
1.2
, y2
3.273
X3 =
i
1.3
Y3 =
i
4.50283
X4
i
1.4
6.7162
X5 =
i
1.5
Y5 =
i
11.4427
eTextbook and Media
Assistance Used
Hint
Assistance Used
The vector field is given by v = y i + 1.1x² j , that is, the flow line (x (t), y (t)) satisfies
x' (t)
= y²
y' (t) = 1.1x².
Only problem 30
7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where
F2 vanishes. Plot a few flow lines.
8. Repeat the previous problem for F = yî + (x − y)î.
Chapter 13 Solutions
Calculus
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- 1-6 Sketch the vector field F by drawing a diagram as in figure 3. F(x,y)=(xy)i+xjarrow_forwardA4. Which of the following vector fields is not the curl of another vector field? A. F=zi+zj+yk B. F= ²1-2ryj+5k C. F=3ri-2yj-zk D. F=zi+yj+zk E. F= 21+2+4k Contiarrow_forwardIncorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i + 1.1x² j using 5 steps with At = 0.1. Find the exact values of x1,.…. ,X5 and yı, , y5 and then fill in the blanks rounding your numbers to •.... three decimal places. X1 = i 1.1 ,Yi = i 2.51 X2 i 1.2 ,y2 3.273 X3 = i 1.3 ,Y3 = i 4.50283 X4 = i 1.4 , Y4 i 6.7162 X5 = i 1.5 , Y5 = i 11.4427 eTextbook and Media Hint I| ||arrow_forward
- 5. If vector T = (x + y +1)i + j - (x + y)k then T.curl(T )isarrow_forward1. Let F(x, y, z) be the vector field (r, 2r, 2y2) and C be the curve parameterized by r(t) = (cos(t), sin(t), t), for 0 ≤t≤ 2. Compute f F drarrow_forward1. Determine if the following statements are True or False. Support your answer. (a) If F = xi + yj + zk and C is the straight line from (3, 3, 3) to the origin, then fF- dr is positive. (b) If C is a simple curve in R?, then f Vf - dr = 0. (c) If F is conservative vector field in R, then curl F = 0. (d) fxdx+ ydy + zdz = 0, for all simple, closed curves C in R3. (e) The iterated integral + y² + z +5 dz dy dx is given by an equivalent integral in spherical coordinates as a/4 +5 sin o dp do d0.arrow_forward
- 6.2. Let F be a vector field defined on all of R³, except at the two points p q = (-2,0,0). Let S1, S2, and S be the following spheres, centered at (2,0, 0), (–2,0,0), and (0,0, 0), respectively, each oriented by the outward normal. (2,0,0) and Sı: (x – 2)2 + y + 2² = 1 S2: (x + 2)? + y² + z² = 1 T² + y? + z? = 25 S: Assume that V ·F = 0. If ffs, F dS = 5 and ffs F. dS = 6, what is ffs F· dS?arrow_forwardplease help mearrow_forwardLet C, V, and£, be the oriented curves in Figure 16, and let F = V f be a gradient vector field such that fc F • dr = 4. What are the values of the following integrals? (a) fv F • dr (b) L F. drarrow_forward
- Compute fa F - dr where F = (x+ y)i + yj and C is the quarter unit circle, oriented counter- clockwise as shown in Figure 18.22. Example 1 %3D Figure 18.22: The vector field F = (x+y)i +yj and the quarter circle C %3Darrow_forward17. Verify Stokes's Theorem for the following vector field E = xyâ – (x² + 2y²)ây - for the contour shown below. Recall Stokes's Theorem: Ē - ai = [[ (v x E) · dš E di || (v x E) · dš C S yarrow_forward6. The figure here shows the vector field Vf, where f is con- tinuously differentiable in the whole plane. The two ends of an oriented curve C from P to Q are shown, but the middle portion of the path is outside the viewing window. The line integral Vf.dr is A. positive. B. negative. C. zero. D. Can't tell without further informationarrow_forward
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