CALCULUS (CLOTH)
4th Edition
ISBN: 9781319050733
Author: Rogawski
Publisher: MAC HIGHER
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Chapter 16.5, Problem 33E
To determine
\To calculate:
for the Disk D.
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For number 9
The answer is A
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The answer is B,
Could you please show the steps to obtain the answer
2. Suppose that U(x, y, z) = x² + y²+ z² represents the temperature of a 3-dimensional solid object
at any point (x, y, z). Then
F(x, y, z) = -KVU (x, y, z)
represents the heat flow at (x, y, z) where K > 0 is called the conductivity constant and the
negative sign indicates that the heat moves from higher temperature region into lower temperature
region. Answer the following questions.
(A) [90%] Compute the inward heat flux (i.e., the inward flux of F) across the surface z =
1 - x² - y².
(B) [10%] Use the differential operator(s) to determine if the heat flow is rotational or irrotational.
Chapter 16 Solutions
CALCULUS (CLOTH)
Ch. 16.1 - Prob. 1PQCh. 16.1 - Prob. 2PQCh. 16.1 - Prob. 3PQCh. 16.1 - Prob. 4PQCh. 16.1 - Prob. 5PQCh. 16.1 - Prob. 6PQCh. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4E
Ch. 16.1 - Prob. 5ECh. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Prob. 8ECh. 16.1 - Prob. 9ECh. 16.1 - Prob. 10ECh. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Prob. 16ECh. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Prob. 20ECh. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Prob. 34ECh. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Prob. 44ECh. 16.1 - Prob. 45ECh. 16.1 - Prob. 46ECh. 16.1 - Prob. 47ECh. 16.1 - Prob. 48ECh. 16.1 - Prob. 49ECh. 16.1 - Prob. 50ECh. 16.1 - Prob. 51ECh. 16.1 - Prob. 52ECh. 16.1 - Prob. 53ECh. 16.1 - Prob. 54ECh. 16.1 - Prob. 55ECh. 16.2 - Prob. 1PQCh. 16.2 - Prob. 2PQCh. 16.2 - Prob. 3PQCh. 16.2 - Prob. 4PQCh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Prob. 32ECh. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.2 - Prob. 49ECh. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.2 - Prob. 53ECh. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - Prob. 57ECh. 16.2 - Prob. 58ECh. 16.2 - Prob. 59ECh. 16.2 - Prob. 60ECh. 16.2 - Prob. 61ECh. 16.2 - Prob. 62ECh. 16.2 - Prob. 63ECh. 16.2 - Prob. 64ECh. 16.2 - Prob. 65ECh. 16.2 - Prob. 66ECh. 16.2 - Prob. 67ECh. 16.2 - Prob. 68ECh. 16.2 - Prob. 69ECh. 16.2 - Prob. 70ECh. 16.3 - Prob. 1PQCh. 16.3 - Prob. 2PQCh. 16.3 - Prob. 3PQCh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Prob. 20ECh. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Prob. 28ECh. 16.3 - Prob. 29ECh. 16.3 - Prob. 30ECh. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.3 - Prob. 42ECh. 16.3 - Prob. 43ECh. 16.3 - Prob. 44ECh. 16.3 - Prob. 45ECh. 16.3 - Prob. 46ECh. 16.4 - Prob. 1PQCh. 16.4 - Prob. 2PQCh. 16.4 - Prob. 3PQCh. 16.4 - Prob. 4PQCh. 16.4 - Prob. 5PQCh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Prob. 25ECh. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Prob. 33ECh. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Prob. 43ECh. 16.4 - Prob. 44ECh. 16.4 - Prob. 45ECh. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.4 - Prob. 49ECh. 16.4 - Prob. 50ECh. 16.4 - Prob. 51ECh. 16.4 - Prob. 52ECh. 16.4 - Prob. 53ECh. 16.4 - Prob. 54ECh. 16.4 - Prob. 55ECh. 16.4 - Prob. 56ECh. 16.4 - Prob. 57ECh. 16.4 - Prob. 58ECh. 16.4 - Prob. 59ECh. 16.4 - Prob. 60ECh. 16.5 - Prob. 1PQCh. 16.5 - Prob. 2PQCh. 16.5 - Prob. 3PQCh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - Prob. 8ECh. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - Prob. 14ECh. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - Prob. 17ECh. 16.5 - Prob. 18ECh. 16.5 - Prob. 19ECh. 16.5 - Prob. 20ECh. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - Prob. 23ECh. 16.5 - Prob. 24ECh. 16.5 - Prob. 25ECh. 16.5 - Prob. 26ECh. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Prob. 29ECh. 16.5 - Prob. 30ECh. 16.5 - Prob. 31ECh. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.5 - Prob. 35ECh. 16.5 - Prob. 36ECh. 16.5 - Prob. 37ECh. 16.5 - Prob. 38ECh. 16.5 - Prob. 39ECh. 16.5 - Prob. 40ECh. 16.5 - Prob. 41ECh. 16.5 - Prob. 42ECh. 16.5 - Prob. 43ECh. 16.5 - Prob. 44ECh. 16.5 - Prob. 45ECh. 16.5 - Prob. 46ECh. 16.5 - Prob. 47ECh. 16.5 - Prob. 48ECh. 16.5 - Prob. 49ECh. 16.5 - Prob. 50ECh. 16.5 - Prob. 51ECh. 16.5 - Prob. 52ECh. 16.5 - Prob. 53ECh. 16.5 - Prob. 54ECh. 16.5 - Prob. 55ECh. 16.5 - Prob. 56ECh. 16.5 - Prob. 57ECh. 16.5 - Prob. 58ECh. 16.5 - Prob. 59ECh. 16.5 - Prob. 60ECh. 16.5 - Prob. 61ECh. 16.5 - Prob. 62ECh. 16.5 - Prob. 63ECh. 16.5 - Prob. 64ECh. 16.5 - Prob. 65ECh. 16.5 - Prob. 66ECh. 16.6 - Prob. 1PQCh. 16.6 - Prob. 2PQCh. 16.6 - Prob. 3PQCh. 16.6 - Prob. 4PQCh. 16.6 - Prob. 1ECh. 16.6 - Prob. 2ECh. 16.6 - Prob. 3ECh. 16.6 - Prob. 4ECh. 16.6 - Prob. 5ECh. 16.6 - Prob. 6ECh. 16.6 - Prob. 7ECh. 16.6 - Prob. 8ECh. 16.6 - Prob. 9ECh. 16.6 - Prob. 10ECh. 16.6 - Prob. 11ECh. 16.6 - Prob. 12ECh. 16.6 - Prob. 13ECh. 16.6 - Prob. 14ECh. 16.6 - Prob. 15ECh. 16.6 - Prob. 16ECh. 16.6 - Prob. 17ECh. 16.6 - Prob. 18ECh. 16.6 - Prob. 19ECh. 16.6 - Prob. 20ECh. 16.6 - Prob. 21ECh. 16.6 - Prob. 22ECh. 16.6 - Prob. 23ECh. 16.6 - Prob. 24ECh. 16.6 - Prob. 25ECh. 16.6 - Prob. 26ECh. 16.6 - Prob. 27ECh. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Prob. 30ECh. 16.6 - Prob. 31ECh. 16.6 - Prob. 32ECh. 16.6 - Prob. 33ECh. 16.6 - Prob. 34ECh. 16.6 - Prob. 35ECh. 16.6 - Prob. 36ECh. 16.6 - Prob. 37ECh. 16.6 - Prob. 38ECh. 16.6 - Prob. 39ECh. 16.6 - Prob. 40ECh. 16.6 - Prob. 41ECh. 16.6 - Prob. 42ECh. 16.6 - Prob. 43ECh. 16.6 - Prob. 44ECh. 16.6 - Prob. 45ECh. 16.6 - Prob. 46ECh. 16.6 - Prob. 47ECh. 16.6 - Prob. 48ECh. 16.6 - Prob. 49ECh. 16.6 - Prob. 50ECh. 16.6 - Prob. 51ECh. 16.6 - Prob. 52ECh. 16 - Prob. 1CRECh. 16 - Prob. 2CRECh. 16 - Prob. 3CRECh. 16 - Prob. 4CRECh. 16 - Prob. 5CRECh. 16 - Prob. 6CRECh. 16 - Prob. 7CRECh. 16 - Prob. 8CRECh. 16 - Prob. 9CRECh. 16 - Prob. 10CRECh. 16 - Prob. 11CRECh. 16 - Prob. 12CRECh. 16 - Prob. 13CRECh. 16 - Prob. 14CRECh. 16 - Prob. 15CRECh. 16 - Prob. 16CRECh. 16 - Prob. 17CRECh. 16 - Prob. 18CRECh. 16 - Prob. 19CRECh. 16 - Prob. 20CRECh. 16 - Prob. 21CRECh. 16 - Prob. 22CRECh. 16 - Prob. 23CRECh. 16 - Prob. 24CRECh. 16 - Prob. 25CRECh. 16 - Prob. 26CRECh. 16 - Prob. 27CRECh. 16 - Prob. 28CRECh. 16 - Prob. 29CRECh. 16 - Prob. 30CRECh. 16 - Prob. 31CRECh. 16 - Prob. 32CRECh. 16 - Prob. 33CRECh. 16 - Prob. 34CRECh. 16 - Prob. 35CRECh. 16 - Prob. 36CRECh. 16 - Prob. 37CRECh. 16 - Prob. 38CRECh. 16 - Prob. 39CRECh. 16 - Prob. 40CRECh. 16 - Prob. 41CRECh. 16 - Prob. 42CRECh. 16 - Prob. 43CRECh. 16 - Prob. 44CRECh. 16 - Prob. 45CRECh. 16 - Prob. 46CRECh. 16 - Prob. 47CRECh. 16 - Prob. 48CRECh. 16 - Prob. 49CRECh. 16 - Prob. 50CRECh. 16 - Prob. 51CRECh. 16 - Prob. 52CRECh. 16 - Prob. 53CRECh. 16 - Prob. 54CRECh. 16 - Prob. 55CRECh. 16 - Prob. 56CRECh. 16 - Prob. 57CRECh. 16 - Prob. 58CRECh. 16 - Prob. 59CRECh. 16 - Prob. 60CRECh. 16 - Prob. 61CRE
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