Finite Mathematics
7th Edition
ISBN: 9781337280426
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Chapter 0.6, Problem 26E
To determine
To calculate: The solution of the equation
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16.4. Show that if z' is the principal value, then
1+e**
z'dz =
(1-i),
2
where is the upper semicircle from z = 1 to z = -1.
L
16.8. For each of the following functions f, describe the domain of ana-
lyticity and apply the Cauchy-Goursat Theorem to show that f(z)dz =
0, where is the circle |2|=1:1
(a). f(z) =
1
z 2 + 2x + 2
(b). f(z) = ze*.
What about (c). f(z) = (2z-i)-2?
16.3. Evaluate each of the following integrals where the path is an
arbitrary contour between the limits of integrations
(a). [1
ri/2
edz, (b).
(b). La cos
COS
(2) d
dz, (c). (z−3)³dz.
0
Chapter 0 Solutions
Finite Mathematics
Ch. 0.1 - Prob. 1ECh. 0.1 - Prob. 2ECh. 0.1 - Prob. 3ECh. 0.1 - Prob. 4ECh. 0.1 - Prob. 5ECh. 0.1 - Prob. 6ECh. 0.1 - Prob. 7ECh. 0.1 - Prob. 8ECh. 0.1 - Prob. 9ECh. 0.1 - Prob. 10E
Ch. 0.1 - Prob. 11ECh. 0.1 - Prob. 12ECh. 0.1 - Prob. 13ECh. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 15ECh. 0.1 - Prob. 16ECh. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 19ECh. 0.1 - Prob. 20ECh. 0.1 - Prob. 21ECh. 0.1 - Prob. 22ECh. 0.1 - Prob. 23ECh. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 25ECh. 0.1 - Prob. 26ECh. 0.1 - Prob. 27ECh. 0.1 - Prob. 28ECh. 0.1 - Prob. 29ECh. 0.1 - Prob. 30ECh. 0.1 - Prob. 31ECh. 0.1 - Prob. 32ECh. 0.1 - Prob. 33ECh. 0.1 - Prob. 34ECh. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Prob. 38ECh. 0.1 - Prob. 39ECh. 0.1 - Prob. 40ECh. 0.1 - Prob. 41ECh. 0.1 - Prob. 42ECh. 0.1 - Prob. 43ECh. 0.1 - Prob. 44ECh. 0.1 - Prob. 45ECh. 0.1 - Prob. 46ECh. 0.1 - Prob. 47ECh. 0.1 - Prob. 48ECh. 0.1 - Prob. 49ECh. 0.1 - Prob. 50ECh. 0.2 - Prob. 1ECh. 0.2 - Prob. 2ECh. 0.2 - Prob. 3ECh. 0.2 - Prob. 4ECh. 0.2 - Prob. 5ECh. 0.2 - Prob. 6ECh. 0.2 - Prob. 7ECh. 0.2 - Prob. 8ECh. 0.2 - Prob. 9ECh. 0.2 - Prob. 10ECh. 0.2 - Prob. 11ECh. 0.2 - Prob. 12ECh. 0.2 - Prob. 13ECh. 0.2 - Prob. 14ECh. 0.2 - Prob. 15ECh. 0.2 - Prob. 16ECh. 0.2 - Prob. 17ECh. 0.2 - Prob. 18ECh. 0.2 - Prob. 19ECh. 0.2 - Prob. 20ECh. 0.2 - Prob. 21ECh. 0.2 - Prob. 22ECh. 0.2 - Prob. 23ECh. 0.2 - Prob. 24ECh. 0.2 - Prob. 25ECh. 0.2 - Prob. 26ECh. 0.2 - Prob. 27ECh. 0.2 - Prob. 28ECh. 0.2 - Prob. 29ECh. 0.2 - Prob. 30ECh. 0.2 - Prob. 31ECh. 0.2 - Prob. 32ECh. 0.2 - Prob. 33ECh. 0.2 - Prob. 34ECh. 0.2 - Convert the expressions in Exercises 31-36 to...Ch. 0.2 - Prob. 36ECh. 0.2 - Prob. 37ECh. 0.2 - Prob. 38ECh. 0.2 - Prob. 39ECh. 0.2 - Prob. 40ECh. 0.2 - Prob. 41ECh. 0.2 - Prob. 42ECh. 0.2 - Prob. 43ECh. 0.2 - Prob. 44ECh. 0.2 - Prob. 45ECh. 0.2 - Prob. 46ECh. 0.2 - Prob. 47ECh. 0.2 - Evaluate expressions in Exercises 3756, rounding...Ch. 0.2 - Prob. 49ECh. 0.2 - Prob. 50ECh. 0.2 - Prob. 51ECh. 0.2 - Prob. 52ECh. 0.2 - Prob. 53ECh. 0.2 - Prob. 54ECh. 0.2 - Prob. 55ECh. 0.2 - Prob. 56ECh. 0.2 - Prob. 57ECh. 0.2 - Prob. 58ECh. 0.2 - Prob. 59ECh. 0.2 - Prob. 60ECh. 0.2 - Prob. 61ECh. 0.2 - Prob. 62ECh. 0.2 - Prob. 63ECh. 0.2 - Prob. 64ECh. 0.2 - Prob. 65ECh. 0.2 - Prob. 66ECh. 0.2 - Prob. 67ECh. 0.2 - Prob. 68ECh. 0.2 - Prob. 69ECh. 0.2 - Prob. 70ECh. 0.2 - Prob. 71ECh. 0.2 - Prob. 72ECh. 0.2 - Prob. 73ECh. 0.2 - Prob. 74ECh. 0.2 - Prob. 75ECh. 0.2 - Prob. 76ECh. 0.2 - Prob. 77ECh. 0.2 - Prob. 78ECh. 0.2 - Prob. 79ECh. 0.2 - Prob. 80ECh. 0.2 - Prob. 81ECh. 0.2 - Prob. 82ECh. 0.2 - Prob. 83ECh. 0.2 - Prob. 84ECh. 0.2 - Prob. 85ECh. 0.2 - Prob. 86ECh. 0.2 - Prob. 87ECh. 0.2 - Prob. 88ECh. 0.2 - Prob. 89ECh. 0.2 - Prob. 90ECh. 0.2 - Prob. 91ECh. 0.2 - Prob. 92ECh. 0.2 - Prob. 93ECh. 0.2 - Prob. 94ECh. 0.2 - Prob. 95ECh. 0.2 - Prob. 96ECh. 0.2 - Prob. 97ECh. 0.2 - Prob. 98ECh. 0.2 - Prob. 99ECh. 0.2 - Prob. 100ECh. 0.2 - Prob. 101ECh. 0.2 - Prob. 102ECh. 0.2 - Prob. 103ECh. 0.2 - Prob. 104ECh. 0.2 - Prob. 105ECh. 0.2 - Prob. 106ECh. 0.2 - Prob. 107ECh. 0.2 - Prob. 108ECh. 0.2 - Prob. 109ECh. 0.2 - Prob. 110ECh. 0.2 - Prob. 111ECh. 0.2 - Prob. 112ECh. 0.2 - Prob. 113ECh. 0.2 - Prob. 114ECh. 0.2 - Prob. 115ECh. 0.2 - Prob. 116ECh. 0.2 - Prob. 117ECh. 0.2 - Prob. 118ECh. 0.2 - Prob. 119ECh. 0.2 - Prob. 120ECh. 0.3 - Expand each expression in Exercises 122. x(4x+6)Ch. 0.3 - Prob. 2ECh. 0.3 - Prob. 3ECh. 0.3 - Prob. 4ECh. 0.3 - Prob. 5ECh. 0.3 - Prob. 6ECh. 0.3 - Prob. 7ECh. 0.3 - Prob. 8ECh. 0.3 - Prob. 9ECh. 0.3 - Prob. 10ECh. 0.3 - Prob. 11ECh. 0.3 - Prob. 12ECh. 0.3 - Prob. 13ECh. 0.3 - Prob. 14ECh. 0.3 - Prob. 15ECh. 0.3 - Prob. 16ECh. 0.3 - Expand each expression in Exercises 122....Ch. 0.3 - Prob. 18ECh. 0.3 - Prob. 19ECh. 0.3 - Prob. 20ECh. 0.3 - Prob. 21ECh. 0.3 - Prob. 22ECh. 0.3 - Prob. 23ECh. 0.3 - Prob. 24ECh. 0.3 - In Exercises 2330, factor each expression and...Ch. 0.3 - Prob. 26ECh. 0.3 - Prob. 27ECh. 0.3 - Prob. 28ECh. 0.3 - Prob. 29ECh. 0.3 - In Exercises 2330, factor each expression and...Ch. 0.3 - Prob. 31ECh. 0.3 - Prob. 32ECh. 0.3 - Prob. 33ECh. 0.3 - Prob. 34ECh. 0.3 - Prob. 35ECh. 0.3 - In Exercises 3148, (a) factor the given...Ch. 0.3 - Prob. 37ECh. 0.3 - Prob. 38ECh. 0.3 - Prob. 39ECh. 0.3 - In Exercises 3148, (a) factor the given...Ch. 0.3 - Prob. 41ECh. 0.3 - Prob. 42ECh. 0.3 - Prob. 43ECh. 0.3 - Prob. 44ECh. 0.3 - Prob. 45ECh. 0.3 - Prob. 46ECh. 0.3 - Prob. 47ECh. 0.3 - Prob. 48ECh. 0.4 - Prob. 1ECh. 0.4 - Prob. 2ECh. 0.4 - Prob. 3ECh. 0.4 - Prob. 4ECh. 0.4 - Prob. 5ECh. 0.4 - Prob. 6ECh. 0.4 - Prob. 7ECh. 0.4 - Prob. 8ECh. 0.4 - Prob. 9ECh. 0.4 - Prob. 10ECh. 0.4 - Prob. 11ECh. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 13ECh. 0.4 - Prob. 14ECh. 0.4 - Prob. 15ECh. 0.4 - Prob. 16ECh. 0.5 - Solve the equations in Exercises 112 for x...Ch. 0.5 - Prob. 2ECh. 0.5 - Prob. 3ECh. 0.5 - Prob. 4ECh. 0.5 - Prob. 5ECh. 0.5 - Prob. 6ECh. 0.5 - Prob. 7ECh. 0.5 - Prob. 8ECh. 0.5 - Prob. 9ECh. 0.5 - Prob. 10ECh. 0.5 - Prob. 11ECh. 0.5 - Solve the equations in Exercises 112 for x...Ch. 0.5 - Prob. 13ECh. 0.5 - Prob. 14ECh. 0.5 - Prob. 15ECh. 0.5 - Prob. 16ECh. 0.5 - Prob. 17ECh. 0.5 - Prob. 18ECh. 0.5 - Prob. 19ECh. 0.5 - Prob. 20ECh. 0.5 - Prob. 21ECh. 0.5 - Prob. 22ECh. 0.5 - Prob. 23ECh. 0.5 - Prob. 24ECh. 0.5 - Prob. 25ECh. 0.5 - Prob. 26ECh. 0.5 - Prob. 27ECh. 0.5 - Prob. 28ECh. 0.5 - Prob. 29ECh. 0.5 - Prob. 30ECh. 0.5 - Prob. 31ECh. 0.5 - Prob. 32ECh. 0.5 - Prob. 33ECh. 0.5 - Prob. 34ECh. 0.5 - Prob. 35ECh. 0.5 - Prob. 36ECh. 0.5 - Find all possible real solutions of each equation...Ch. 0.5 - Prob. 38ECh. 0.5 - Prob. 39ECh. 0.5 - Find all possible real solutions of each equation...Ch. 0.5 - Prob. 41ECh. 0.5 - Prob. 42ECh. 0.5 - Prob. 43ECh. 0.5 - Prob. 44ECh. 0.6 - Prob. 1ECh. 0.6 - Prob. 2ECh. 0.6 - Prob. 3ECh. 0.6 - Prob. 4ECh. 0.6 - Prob. 5ECh. 0.6 - Prob. 6ECh. 0.6 - Prob. 7ECh. 0.6 - Prob. 8ECh. 0.6 - Prob. 9ECh. 0.6 - Prob. 10ECh. 0.6 - Solve the equations in Exercises 126....Ch. 0.6 - Prob. 12ECh. 0.6 - Prob. 13ECh. 0.6 - Prob. 14ECh. 0.6 - Prob. 15ECh. 0.6 - Prob. 16ECh. 0.6 - Prob. 17ECh. 0.6 - Prob. 18ECh. 0.6 - Prob. 19ECh. 0.6 - Prob. 20ECh. 0.6 - Prob. 21ECh. 0.6 - Prob. 22ECh. 0.6 - Prob. 23ECh. 0.6 - Prob. 24ECh. 0.6 - Prob. 25ECh. 0.6 - Prob. 26ECh. 0.7 - Referring to the following figure, determine the...Ch. 0.7 - Prob. 2ECh. 0.7 - Prob. 3ECh. 0.7 - Prob. 4ECh. 0.7 - Prob. 5ECh. 0.7 - Prob. 6ECh. 0.7 - Prob. 7ECh. 0.7 - Prob. 8ECh. 0.7 - Prob. 9ECh. 0.7 - Prob. 10ECh. 0.7 - Prob. 11ECh. 0.7 - Prob. 12ECh. 0.7 - Prob. 13ECh. 0.7 - Prob. 14ECh. 0.7 - Prob. 15ECh. 0.7 - Prob. 16ECh. 0.7 - Prob. 17ECh. 0.7 - Find the value of k such that (k,k) is equidistant...Ch. 0.7 - Describe the set of points (x,y) such that...Ch. 0.7 - Prob. 20ECh. 0.8 - In Exercises 14, complete the given tables....Ch. 0.8 - In Exercises 14, complete the given tables....Ch. 0.8 - In Exercises 14, complete the given tables....Ch. 0.8 - In Exercises 14, complete the given tables....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - Prob. 14ECh. 0.8 - Prob. 15ECh. 0.8 - In Exercises 516, evaluate the given quantity....Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - Prob. 23ECh. 0.8 - Prob. 24ECh. 0.8 - Prob. 25ECh. 0.8 - Prob. 26ECh. 0.8 - Prob. 27ECh. 0.8 - Prob. 28ECh. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Prob. 30ECh. 0.8 - Prob. 31ECh. 0.8 - Prob. 32ECh. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Prob. 34ECh. 0.8 - Prob. 35ECh. 0.8 - Prob. 36ECh. 0.8 - Prob. 37ECh. 0.8 - Prob. 38ECh. 0.8 - Prob. 39ECh. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...Ch. 0.8 - In Exercises 4756, solve the given equation for...
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- Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answerarrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answerarrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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