Calculus (MindTap Course List)
11th Edition
ISBN: 9781337275347
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Chapter 4.5, Problem 84E
(a)
To determine
To calculate: The maximum flow rate and the time of its occurrencefrom the provided graph
(b)
To determine
The explanation to calculate the amount of water used in the day from the provided graph
(c)
To determine
To calculate: The two-hour time period when the least amount of water is used and also explain the reason from the provided graph
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Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
21. Determine for which values of m the function (x) = x™ is a solution to the given equation.
a. 3x2
d²y
dx²
b. x2 d²y
+11x
dy
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dx
dy
dx2
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= 0
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