HW10_solution

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University of Massachusetts, Lowell *

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3640

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Electrical Engineering

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Jan 9, 2024

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University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10 Evaluate the following integrals using Cauchy Residue Theory. All closed contours are traversed CCW. For questions 1 – 3, evaluate on the given contours. Question #1) C: |𝑧 + 2𝑖 − 1| = 3 Question #2) C: |𝑧 − 𝑖| = 3 Question #3) C: |𝑧 + 1 2 | = 1 For questions 4 – 6, evaluate on the given contours. Question #4) C: |𝑧 − 2.5| = 3 Question #5) C: |𝑧 − 2 + 2𝑖| = 3 Question #6) C: |𝑧 + 2 − 2𝑖| = 3 Question #7) 𝐼 = Question #8) 𝐼 = Question #9) 𝐼 = Question #10) 𝐼 = All answers to the Blackboard thing are multiple choice. Note Well! The answers are the ABSOLUTE VALUE of the integral. 𝐼 = ∮ 1 𝑧 4 − 1 𝐶 𝑑𝑧 𝐼 = ∮ 1 (𝑧 − 1)(𝑧 + 2) 2 𝐶 𝑑𝑧 ∫ 𝑑𝜃 2 − sin 𝜃 2𝜋 0 ∫ sin 2 𝜃 5 + 3 cos 𝜃 𝑑𝜃 2𝜋 0 ∫ 1 𝑥 2 + 2𝑥 + 5 𝑑𝑥 ∞ −∞ ∫ 1 𝑥 3 − 𝑥 2 − 𝑥 − 15 𝑑𝑥 ∞ −∞
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10 Question 1) Choose |𝐼| from the following: a. 0.6323 b. 0.6449 c. 0.6578 d. 0.6710 e. 0.6844 f. 0.6981 * g. 0.7121 h. 0.7263 Question 2) Choose |𝐼| from the following: a. 0.0 * b. 0.5 c. 1.0 d. 1.5 e. 2.0 f. 2.5 g. 3.0 h. 3.5 Question 3) Choose |𝐼| from the following: a. 0.0 * b. 0.5π c. 1.0π d. 1.5π e. 2.0π f. 2.5π g. 3.0π h. 3.5π Question 4) Choose |𝐼| from the following: a. 1.5708 * b. 1.6022 c. 1.6343 d. 1.6669 e. 1.7003 f. 1.7343 g. 1.7690 h. 1.8044 Answers: 1 f 2 a 3 a 4 a 5 g 6 a 7 g 8 g 9 e 10 h
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10 Question 5) Choose |𝐼| from the following: a. 1.971 b. 2.012 c. 2.052 d. 2.093 e. 2.135 f. 2.177 g. 2.221 * h. 2.265 Question 6) Choose |𝐼| from the following: a. 2.221 * b. 2.266 c. 2.311 d. 2.357 e. 2.404 f. 2.452 g. 2.501 h. 2.551 Question 7) Choose |𝐼| from the following: a. 3.2212 b. 3.2856 c. 3.3513 d. 3.4184 e. 3.4867 f. 3.5565 g. 3.6276 * h. 3.7002
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University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10 Question 8) Choose |𝐼| from the following: a. 0.6199 b. 0.6323 c. 0.6450 d. 0.6579 e. 0.6710 f. 0.6844 g. 0.6981 * h. 0.7121 Question 9) Choose |𝐼| from the following: a. 1.451 b. 1.480 c. 1.510 d. 1.540 e. 1.571 * f. 1.602 g. 1.634 h. 1.667 Question 10) Choose |𝐼| from the following: a. 0.273 b. 0.279 c. 0.285 d. 0.290 e. 0.296 f. 0.302 g. 0.308 h. 0.314 *
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
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University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
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Eager to read complete document? Join bartleby learn and gain access to the full version
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University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10
University of Massachusetts, Lowell 301 Ball Hall One University Avenue Lowell, Massachusetts 01854 Phone: (978) 934-3300 Fax: (978) 934-3027 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EECE 3640 Engineering Math Homework #10

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