
CALCULUS+ITS APPLICATIONS (LL)
12th Edition
ISBN: 9780135165928
Author: BITTINGER
Publisher: PEARSON
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Chapter E, Problem 16E
To determine
To Calculate:
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(9) (16 points) Let
F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k
=
-
= (x²+y4,3xy, 2x2 + 2²).
(a) (4 points) Calculate the divergence and curl of F.
(b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² =
16, z ≥ 0.
(c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] ×
[0,1] x [0,1].
(8) (12 points)
(a) (8 points) Let C be the circle x² + y² = 4. Let
F(x, y) = (2y + e²)i + (x + sin(y²))j.
Evaluate the line integral
JF.
F.ds.
Hint: First calculate V x F.
(b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux
integral
√(V × F)
F).dS.
Justify your answer.
Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle.
a = 13, b = 15, C = 68°
Law of Sines
Law of Cosines
Then solve the triangle. (Round your answers to four decimal places.)
C = 15.7449
A = 49.9288
B = 62.0712
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Chapter E Solutions
CALCULUS+ITS APPLICATIONS (LL)
Ch. E - Prob. 1ECh. E - Prob. 2ECh. E - Prob. 3ECh. E - Prob. 4ECh. E - Prob. 5ECh. E - Prob. 6ECh. E - Prob. 7ECh. E - Prob. 8ECh. E - Prob. 9ECh. E - Prob. 10E
Ch. E - Solve each integral using Table 1. 11. In3xdx,x0Ch. E - Solve each integral using Table 1. 12. In45xdx,x0Ch. E - Solve each integral using Table 1. 13. x4Inxdx,x0Ch. E - Prob. 14ECh. E - Prob. 15ECh. E - Prob. 16ECh. E - Prob. 17ECh. E - Prob. 18ECh. E - Prob. 19ECh. E - Prob. 20ECh. E - Prob. 21ECh. E - Solve each integral using Table 1. 22. 9t21dtCh. E - Solve each integral using Table 1. 23. 4m2+16dmCh. E - Solve each integral using Table 1. 24. 3inxx2dxCh. E - Prob. 25ECh. E - Prob. 26ECh. E - Prob. 27ECh. E - Prob. 28ECh. E - Prob. 29ECh. E - Prob. 30ECh. E - Prob. 31ECh. E - Prob. 32ECh. E - Evaluate using Table 1 33. 83x22xdxCh. E - Evaluate using Table 1 34. xdx4x212x+9Ch. E - Evaluate using Table 1 35. dxx34x2+4xCh. E - Prob. 36ECh. E - Prob. 37ECh. E - Prob. 38ECh. E - Prob. 39ECh. E - Prob. 40ECh. E - Prob. 41E
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