Practical Business Math Procedures
12th Edition
ISBN: 9781259540554
Author: Jeffrey Slater, Sharon Wittry
Publisher: McGraw-Hill Education
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Chapter 17.2, Problem 5AH
To determine
To prepare: the depreciation schedule by using the given data.
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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)
3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M
a simple module?
(b) State and prove Schur's Lemma for simple modules.
(c) Let AM(K) and M = K" the natural A-module.
(i) Show that M is a simple K-module.
(ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a
is a matrix in the centre of M, (K).
[Recall that the centre, Z(M,(K)) == {a Mn(K) | ab
M,,(K)}.]
= ba for all bЄ
(iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~
K as K-algebras.
Is this consistent with Schur's lemma?
Chapter 17 Solutions
Practical Business Math Procedures
Ch. 17.1 - Prepare a depreciation schedule using...Ch. 17.1 - If the truck were bought on February 3, what would...Ch. 17.1 - Prepare a depreciation schedule using...Ch. 17.1 - If the truck were bought on February 3, what would...Ch. 17.1 - Prob. 1AHCh. 17.1 - Find the annual depreciation using the...Ch. 17.1 - Prob. 3AHCh. 17.1 - Find the first-year depreciation to the nearest...Ch. 17.1 - Prob. 5AHCh. 17.1 - Prob. 6AH
Ch. 17.1 - Prob. 7AHCh. 17.1 - Prob. 8AHCh. 17.1 - Prob. 9AHCh. 17.1 - Prob. 10AHCh. 17.1 - Prob. 11AHCh. 17.2 - From the following facts prepare a depreciation...Ch. 17.2 - From the following facts prepare a depreciation...Ch. 17.2 - Prob. 1AHCh. 17.2 - Prob. 2AHCh. 17.2 - Prob. 3AHCh. 17.2 - Prob. 4AHCh. 17.2 - Prob. 5AHCh. 17.2 - Forsmann & Smythe purchased a new machine that...Ch. 17.2 - Young Electrical Company depreciates its vans...Ch. 17.2 - Prob. 8AHCh. 17.3 - Prob. 1PQCh. 17.3 - Prob. 1EPQCh. 17.3 - Prob. 1AHCh. 17.3 - Prob. 2AHCh. 17.3 - Prob. 3AHCh. 17.3 - Prob. 4AHCh. 17.3 - Prob. 5AHCh. 17.3 - Prob. 6AHCh. 17.3 - Prob. 7AHCh. 17.3 - Prob. 8AHCh. 17.3 - Prob. 9AHCh. 17.4 - In 2015, Rancho Corporation bought semiconductor...Ch. 17.4 - Prob. 2PQCh. 17.4 - Prob. 1EPQCh. 17.4 - Prob. 2EPQCh. 17.4 - Prob. 1AHCh. 17.4 - Prob. 2AHCh. 17.4 - Prob. 3AHCh. 17.4 - Prob. 4AHCh. 17.4 - Prob. 5AHCh. 17.4 - Prob. 6AHCh. 17.4 - Wolfe Ltd. purchased a supercomputer for $75,000...Ch. 17.4 - Prob. 8AHCh. 17.4 - Prob. 9AHCh. 17 - Prob. 1ECPCh. 17 - From the following facts, complete a depreciation...Ch. 17 - Prob. 3ECPCh. 17 - Prob. 4ECPCh. 17 - Prob. 5ECPCh. 17 - Prob. 6ECPCh. 17 - From the following facts, complete a depreciation...Ch. 17 - Prob. 8ECPCh. 17 - Prob. 9ECPCh. 17 - Prob. 10ECPCh. 17 - From the following facts, prepare a depreciation...Ch. 17 - Prob. 12ECPCh. 17 - For the first 2 years, calculate the depreciation...Ch. 17 - For the first 2 years, calculate the depreciation...Ch. 17 - Complete the following table given this...Ch. 17 - Prob. 16ECPCh. 17 - Prob. 17ECPCh. 17 - Prob. 18ECPCh. 17 - Prob. 19ECPCh. 17 - Prob. 20ECPCh. 17 - Prob. 21ECPCh. 17 - Prob. 22ECPCh. 17 - Prob. 23ECPCh. 17 - Whole Foods, the world’s leader in natural and...Ch. 17 - Prob. 25ECPCh. 17 - If corporate headquarters for UPS in Atlanta is...Ch. 17 - Prob. 27ECPCh. 17 - Prob. 28ECPCh. 17 - Prob. 1PTCh. 17 - Prob. 2PTCh. 17 - Prob. 3PTCh. 17 - Prob. 4PTCh. 17 - Prob. 5PT
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