MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE
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Author: Lial
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Chapter 13.1, Problem 5E
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Q1lal Let X be an arbitrary infinite set and let r the family of all subsets
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b\ Let X and Y be two topological space and f:X -…
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Automobile Department
Subject :Engineering Analysis
Time: 2 hour
Date:27-11-2022
کورس اول تحليلات
تعمیر )
1st month exam / 1st semester (2022-2023)/11/27
Note: Answer all questions,all questions have same degree.
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1-
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C-1
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(82+28-3),2-
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2-1
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Q3/: Find the Laplace transform of
1,
0≤t<2,
-2t+1,
2≤t<3,
f(t) =
3t,
t-1,
3≤t 5,
t≥ 5
Q4: Find the Fourier series corresponding to the function
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Chapter 13 Solutions
MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE
Ch. 13.1 - Checkpoint 1
Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2
Find each of the...Ch. 13.1 - Prob. 3CPCh. 13.1 - Prob. 4CPCh. 13.1 - Prob. 5CPCh. 13.1 - Prob. 6CPCh. 13.1 - Prob. 7CPCh. 13.1 - Checkpoint 8
The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...
Ch. 13.1 - 3. In your own words, describe what is meant by an...Ch. 13.1 - 4. Explain why the restriction is necessary in...Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Find each of the given antiderivatives. (See...Ch. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Find each of the given antiderivatives. (See...Ch. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Find each of the given antiderivatives. (See...Ch. 13.1 - Find each of the given antiderivatives. (See...Ch. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 37ECh. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - Find each of the given antiderivatives. (See...Ch. 13.1 - Prob. 41ECh. 13.1 - Prob. 42ECh. 13.1 - 43. Find the equation of the curve whose tangent...Ch. 13.1 - 44. The slope of the tangent line to a curve is...Ch. 13.1 - Prob. 45ECh. 13.1 - Work the given problems. (See Examples 8 and 10.)...Ch. 13.1 - 47. NVIDIA Stock The semiconductor corporation...Ch. 13.1 - Prob. 48ECh. 13.1 - Work the given problems. (See Example...Ch. 13.1 - Work the given problems. (See Example...Ch. 13.1 - Prob. 51ECh. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - Prob. 54ECh. 13.1 - Prob. 55ECh. 13.1 - Prob. 56ECh. 13.1 - Prob. 57ECh. 13.1 - Prob. 58ECh. 13.2 - Checkpoint 1
Find du for the given...Ch. 13.2 - Prob. 2CPCh. 13.2 - Prob. 3CPCh. 13.2 - Prob. 4CPCh. 13.2 - Checkpoint 5
Find the given...Ch. 13.2 - Prob. 6CPCh. 13.2 - Prob. 7CPCh. 13.2 - Prob. 8CPCh. 13.2 - 1. Integration by substitution is related to what...Ch. 13.2 - 2. For each of the given integrals, decide what...Ch. 13.2 - Prob. 3ECh. 13.2 - Use substitution to find the given indefinite...Ch. 13.2 - Use substitution to find the given indefinite...Ch. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Use substitution to find the given indefinite...Ch. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Use substitution to find the given indefinite...Ch. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Use substitution to find the given indefinite...Ch. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Work these problems. Round the constant C to two...Ch. 13.2 - Prob. 42ECh. 13.2 - 43. Bicycle Shops The rate of change of the number...Ch. 13.2 - Prob. 44ECh. 13.2 - 45. Marginal Revenue The marginal revenue (in...Ch. 13.2 - Prob. 46ECh. 13.2 - Work these problems. Round the constant C to two...Ch. 13.2 - 48. Human Resources For Nike Inc., the rate of...Ch. 13.3 - Checkpoint 1 Find the antiderivative xe7xdx.Ch. 13.3 - Prob. 2CPCh. 13.3 - Prob. 3CPCh. 13.3 - Prob. 4CPCh. 13.3 - Prob. 5CPCh. 13.3 - Prob. 6CPCh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Prob. 5ECh. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Find the given indefinite integrals. State whether...Ch. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Find each indefinite integral. (See Example 4.)...Ch. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Find each indefinite integral. (See Example 4.)...Ch. 13.3 - Prob. 31ECh. 13.3 - Find each indefinite integral. (See Example 4.)...Ch. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Velocity Work these exercises. (See Example...Ch. 13.3 - Velocity Work these exercises. (See Example 5.) A...Ch. 13.3 - Prob. 39ECh. 13.3 - Prob. 40ECh. 13.3 - Prob. 41ECh. 13.3 - Velocity Work these exercises. (See Example 5.)...Ch. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Work these exercises (See Example 6.) Total...Ch. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Work these exercises (See Example 6.)
49. Pharmacy...Ch. 13.3 - Work these exercises (See Example...Ch. 13.4 - Checkpoint 1
Use figure 13.3 to estimate the...Ch. 13.4 - Prob. 2CPCh. 13.4 - Checkpoint 5
If the marginal revenue from selling...Ch. 13.4 - Prob. 1ECh. 13.4 - In Exercises 1–4, estimate the required areas by...Ch. 13.4 - Prob. 3ECh. 13.4 - In Exercises 1–4, estimate the required areas by...Ch. 13.4 - 5. Explain the difference between an indefinite...Ch. 13.4 - 6. Complete the following statement:
where
Ch. 13.4 - Prob. 7ECh. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - Approximate the area under each curve and above...Ch. 13.4 - 15. Find by using the formula for the area of a...Ch. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Use the numerical integration feature on a...Ch. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Business A marginal revenue function MR(x) (in...Ch. 13.4 - Business A marginal revenue function MR(x) (in...Ch. 13.4 - 27. Distance Traveled An insurance company...Ch. 13.4 - Prob. 29ECh. 13.4 - 30. Estimate the distance traveled by the car in...Ch. 13.4 - Prob. 28ECh. 13.5 - Checkpoint 1
Let
Find the following.
(a)
(b)
Ch. 13.5 - Prob. 2CPCh. 13.5 - Checkpoint 3
Evaluate each definite...Ch. 13.5 - Checkpoint 4
Evaluate the given...Ch. 13.5 - Checkpoint 5
Find
Ch. 13.5 - Checkpoint 6
Find each shaded area.
(a)
(b)
Ch. 13.5 - Checkpoint 7 Use the function in Example 7 to find...Ch. 13.5 - Prob. 8CPCh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 6ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 9ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 11ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 13ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Evaluate each of the given definite integrals....Ch. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Prob. 25ECh. 13.5 - Prob. 26ECh. 13.5 - Prob. 27ECh. 13.5 - Prob. 28ECh. 13.5 - Prob. 29ECh. 13.5 - Prob. 30ECh. 13.5 - Prob. 31ECh. 13.5 - Prob. 32ECh. 13.5 - Find the area of each shaded region. (See Examples...Ch. 13.5 - Find the area of each shaded region. (See Examples...Ch. 13.5 - Prob. 35ECh. 13.5 - Prob. 36ECh. 13.5 - Prob. 37ECh. 13.5 - Prob. 38ECh. 13.5 - Prob. 39ECh. 13.5 - Prob. 40ECh. 13.5 - Prob. 41ECh. 13.5 - Prob. 42ECh. 13.5 - Prob. 43ECh. 13.5 - Prob. 44ECh. 13.5 - Prob. 45ECh. 13.5 - Prob. 46ECh. 13.5 - Prob. 47ECh. 13.5 - Prob. 48ECh. 13.5 - Prob. 49ECh. 13.5 - Prob. 50ECh. 13.5 - Prob. 51ECh. 13.5 - Prob. 52ECh. 13.5 - Prob. 53ECh. 13.5 - Hospital Care The expenditure rate on hospital...Ch. 13.5 - Prob. 55ECh. 13.5 - Natural Gas The rate at which natural gas was...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Prob. 60ECh. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13.6 - Checkpoint 1
In Example 1, find the total repair...Ch. 13.6 - Prob. 2CPCh. 13.6 - Prob. 3CPCh. 13.6 - Prob. 4CPCh. 13.6 - Prob. 5CPCh. 13.6 - Prob. 6CPCh. 13.6 - Prob. 7CPCh. 13.6 - 1. A car-leasing firm must decide how much to...Ch. 13.6 - Prob. 2ECh. 13.6 - Prob. 3ECh. 13.6 - Prob. 4ECh. 13.6 - Work the given exercises. (See Examples 1 and 2.)...Ch. 13.6 - Work the given exercises. (See Examples 1 and...Ch. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Find the area between the two curves. (See Example...Ch. 13.6 - Find the area between the two curves. (See Example...Ch. 13.6 - Find the area between the two curves. (See Example...Ch. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.6 - Prob. 21ECh. 13.6 - Prob. 22ECh. 13.6 - Prob. 23ECh. 13.6 - 24. Natural Science A new smog-control device will...Ch. 13.6 - Prob. 25ECh. 13.6 - Prob. 26ECh. 13.6 - Prob. 27ECh. 13.6 - 28. Business The rate of expenditure (in dollars...Ch. 13.6 - Prob. 29ECh. 13.6 - 30. Natural Science Suppose that, over a 4-hour...Ch. 13.6 - Prob. 31ECh. 13.6 - Present Value Work these exercises. (See Example...Ch. 13.6 - Prob. 33ECh. 13.6 - Prob. 34ECh. 13.6 - Prob. 35ECh. 13.6 - Present Value Work these exercises. (See Example...Ch. 13.6 - Prob. 37ECh. 13.6 - Business Work the given supply-and-demand...Ch. 13.6 - Prob. 39ECh. 13.6 - Prob. 40ECh. 13.6 - Prob. 41ECh. 13.6 - Prob. 42ECh. 13.6 - Prob. 43ECh. 13.6 - Business Work the given supply-and-demand...Ch. 13.7 - Checkpoint 1 Find the particular solution in...Ch. 13.7 - Prob. 2CPCh. 13.7 - Prob. 3CPCh. 13.7 - Prob. 4CPCh. 13.7 - Prob. 5CPCh. 13.7 - Prob. 6CPCh. 13.7 - Prob. 7CPCh. 13.7 - Prob. 8CPCh. 13.7 - Find general solutions for the given differential...Ch. 13.7 - Prob. 2ECh. 13.7 - Prob. 3ECh. 13.7 - Prob. 4ECh. 13.7 - Prob. 5ECh. 13.7 - Prob. 6ECh. 13.7 - Find general solutions for the given differential...Ch. 13.7 - Prob. 8ECh. 13.7 - Prob. 9ECh. 13.7 - Prob. 10ECh. 13.7 - Prob. 11ECh. 13.7 - Prob. 12ECh. 13.7 - Find general solutions for the given differential...Ch. 13.7 - Prob. 14ECh. 13.7 - Prob. 15ECh. 13.7 - Prob. 16ECh. 13.7 - Prob. 17ECh. 13.7 - Prob. 18ECh. 13.7 - Prob. 19ECh. 13.7 - Prob. 20ECh. 13.7 - Prob. 21ECh. 13.7 - Prob. 22ECh. 13.7 - Prob. 23ECh. 13.7 - Prob. 24ECh. 13.7 - Prob. 25ECh. 13.7 - Prob. 26ECh. 13.7 - Prob. 27ECh. 13.7 - Find particular solutions for the given equations....Ch. 13.7 - Prob. 29ECh. 13.7 - Prob. 30ECh. 13.7 - Find particular solutions for the given equations....Ch. 13.7 - Prob. 32ECh. 13.7 - Prob. 33ECh. 13.7 - Prob. 34ECh. 13.7 - 35. Business The marginal productivity of a...Ch. 13.7 - Prob. 36ECh. 13.7 - Prob. 37ECh. 13.7 - Prob. 38ECh. 13.7 - Prob. 39ECh. 13.7 - Prob. 40ECh. 13.7 - 41. Business Sales of a particular product have...Ch. 13.7 - Prob. 42ECh. 13.7 - Prob. 43ECh. 13.7 - Prob. 44ECh. 13.7 - Prob. 45ECh. 13.7 - Prob. 46ECh. 13.7 - Prob. 47ECh. 13.7 - Prob. 48ECh. 13.7 - Prob. 49ECh. 13.7 - Prob. 50ECh. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 44RECh. 13 - Prob. 45RECh. 13 - Prob. 46RECh. 13 - Prob. 47RECh. 13 - Prob. 48RECh. 13 - Prob. 49RECh. 13 - Prob. 50RECh. 13 - Prob. 51RECh. 13 - Prob. 52RECh. 13 - Prob. 53RECh. 13 - Prob. 55RECh. 13 - Prob. 56RECh. 13 - Prob. 59RECh. 13 - Prob. 60RECh. 13 - Prob. 61RECh. 13 - Prob. 62RECh. 13 - Prob. 63RECh. 13 - Prob. 54RECh. 13 - Prob. 69RECh. 13 - Prob. 35RECh. 13 - Prob. 57RECh. 13 - Prob. 58RECh. 13 - Prob. 71RECh. 13 - Prob. 64RECh. 13 - Prob. 65RECh. 13 - Prob. 66RECh. 13 - Prob. 67RECh. 13 - Prob. 68RECh. 13 - Prob. 75RECh. 13 - Prob. 77RECh. 13 - Prob. 78RECh. 13 - Work the given exercises. Population Growth The...Ch. 13 - Prob. 73RECh. 13 - Prob. 74RECh. 13 - Prob. 76RECh. 13 - Prob. 79RECh. 13 - Prob. 80RECh. 13 - Prob. 81RECh. 13 - Prob. 82RECh. 13 - Prob. 83RECh. 13 - Prob. 84RECh. 13 - Prob. 85RECh. 13 - Prob. 86RECh. 13 - Prob. 87RECh. 13 - Prob. 88RECh. 13 - Prob. 89RECh. 13 - Prob. 90RECh. 13 - Prob. 1CECh. 13 - Prob. 2CECh. 13 - Prob. 3CECh. 13 - Prob. 4CE
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- Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.arrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardMinistry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forward
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Publisher:McGraw-Hill Education
Evaluating Indefinite Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=-xHA2RjVkwY;License: Standard YouTube License, CC-BY
Calculus - Lesson 16 | Indefinite and Definite Integrals | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=bMnMzNKL9Ks;License: Standard YouTube License, CC-BY