Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Textbook Question
Chapter 52, Problem 12A
Solve the following exercises:
In
a. Find ∠ HPM.
b. Find ∠ PMK.
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Theorem: show that XCH) = M(E) M" (6) E +
t
Mcfic
S
a
Solution of ODE
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x = ACE) x + g (t) + X (E) - E
5. (a) State the Residue Theorem. Your answer should include all the conditions required
for the theorem to hold.
(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
に
dz.
You must check all of the conditions of any results that you use.
(5 marks)
(c) Evaluate
L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
x²+2x+5
da.
(11 marks)
3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula
for L(y).
(1 mark)
(b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a
contour. Suppose there exists a finite real number M such that |f(z)| < M for
all z in the image of y. Prove that
<
||, f(z)dz| ≤ ML(y).
(3 marks)
(c) State and prove Liouville's theorem. You may use Cauchy's integral formula without
proof.
(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
Let f UC be a holomorphic function such that
0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
Chapter 52 Solutions
Mathematics for Machine Technology
Ch. 52 - Determine the size of 1.Ch. 52 - If ABCD,BCDE , and 1=2725 , what are the sizes of...Ch. 52 - What is the supplement of a 1051344 angle?Ch. 52 - Determine the center diameter of a pinion gear...Ch. 52 - Solve 578=234x.Ch. 52 - Determine the value of 406.442-1/3. Round the...Ch. 52 - Determine which of the following pairs of...Ch. 52 - Solve the following exercises: In ABC and...Ch. 52 - Solve the following exercises: In figure,...Ch. 52 - Solve the following exercises: In ABC and...
Ch. 52 - Solve the following exercises: Use the figure to...Ch. 52 - Solve the following exercises: In HPM,PMJK. a....Ch. 52 - Solve the following exercises: Refer to the figure...Ch. 52 - Solve the following exercises: Refer to the figure...Ch. 52 - Solve the following exercises: In this figure,...Ch. 52 - Solve the following exercises: a. Find x. b. Find...Ch. 52 - Solve the following exercises: a. Find x. b. Find...Ch. 52 - All dimensions are in inches. a. Find 1. b. Find ...Ch. 52 - All dimensions are in millimeters. a. Find x. b....Ch. 52 - All dimensions are in inches. a. Find 1. b. Find...Ch. 52 - Refer to this figure. Using the given values, find...Ch. 52 - Using the figure and these given values, find the...Ch. 52 - Using the figure and these given values, find the...Ch. 52 - Three holes are drilled in the plate shown. All...Ch. 52 - All dimensions are in inches. Round the answers to...Ch. 52 - All dimensions are in inches. Round the answers to...Ch. 52 - Solve the following exercises: A template is...Ch. 52 - Refer to polygon ABCD. a. If 2 = 87.0, find 1. b....Ch. 52 - Use the angle values given. a. If 1 = 114, find 2....Ch. 52 - Use the angle values given to find 2. a. If 1 =...
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