Thomas' Calculus (14th Edition)
14th Edition
ISBN: 9780134438986
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter A.3, Problem 43E
To determine
The pressure under a water at 50 meters distance from the surface.
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2
prove that Dxy #Dx Dy
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
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.
Chapter A.3 Solutions
Thomas' Calculus (14th Edition)
Ch. A.3 - In Exercises 1 and 2, a particle moves from A to B...Ch. A.3 - Prob. 2ECh. A.3 - Describe the graphs of the equations in
Ch. A.3 - Prob. 4ECh. A.3 - Prob. 5ECh. A.3 - Prob. 6ECh. A.3 - Prob. 7ECh. A.3 - Prob. 8ECh. A.3 - Prob. 9ECh. A.3 - Prob. 10E
Ch. A.3 - Prob. 11ECh. A.3 - In Exercises 9–15, write an equation for each line...Ch. A.3 - Prob. 13ECh. A.3 - Prob. 14ECh. A.3 - Prob. 15ECh. A.3 - In Exercises 16 and 17, find the line’s x-and...Ch. A.3 - In Exercises 16 and 17, find the line’s x-and...Ch. A.3 - Is there anything special about the relationship...Ch. A.3 - Prob. 19ECh. A.3 - Prob. 20ECh. A.3 - Prob. 21ECh. A.3 - Prob. 22ECh. A.3 - Prob. 23ECh. A.3 - Prob. 24ECh. A.3 - Prob. 25ECh. A.3 - Prob. 26ECh. A.3 - Prob. 27ECh. A.3 - Prob. 28ECh. A.3 - Prob. 29ECh. A.3 - Prob. 30ECh. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Prob. 33ECh. A.3 - Describe the regions defined by the inequalities...Ch. A.3 - Prob. 35ECh. A.3 - Write a pair of inequalities that describe the...Ch. A.3 - Prob. 37ECh. A.3 - Prob. 38ECh. A.3 - Prob. 39ECh. A.3 - Prob. 40ECh. A.3 - Prob. 41ECh. A.3 - Insulation According to the figure in Exercise 41,...Ch. A.3 - 43. Pressure under water The pressure p...Ch. A.3 - Reflected light A ray of light comes in along the...Ch. A.3 - Prob. 45ECh. A.3 - Prob. 46ECh. A.3 - Prob. 47ECh. A.3 - Show that the triangle with vertices A(0, 0), ,...Ch. A.3 - Prob. 49ECh. A.3 - Prob. 50ECh. A.3 - Prob. 51ECh. A.3 - Prob. 52E
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