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3) Give an example of a function f(z) which has the following properties. Justify your answer. a) A pole of order 3 at Zo= zi with residue & b) A simple pole at Zo-i-3 with residue Sli-3), and an essential singularity at Z₁ = i with residue 6. c) A pole of order 4 at Zo= 4; -1 with residue 5, and a simple pole at Z₁ = -i with residue -/-/- 2. 1.-3. 4) Let the curve C be given by the graph of the function y= f(x) with f(x) = coshx, a) Draw a sketch of the curve b) Give a path 8: [0,1] → [ which has the curve C as its image c) Compute the length L of the curve

3) Give an example of a function f(z) which has the following properties. Justify your answer. a) A pole of order 3 at Zo= zi with residue & b) A simple pole at Zo-i-3 with residue Sli-3), and an essential singularity at Z₁ = i with residue 6. c) A pole of order 4 at Zo= 4; -1 with residue 5, and a simple pole at Z₁ = -i with residue -/-/- 2. 1.-3. 4) Let the curve C be given by the graph of the function y= f(x) with f(x) = coshx, a) Draw a sketch of the curve b) Give a path 8: [0,1] → [ which has the curve C as its image c) Compute the length L of the curve

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is the 3rd-4th time of asking so please attempt as my questions are limited. The questions I need are: 3 part b 4 part c Part of importance: Handwritten not typed, all times of which I have asked this for some reason I don't get it, when it is typed it confuses me as I'm trying to understand the method chronologically and process what is going on, whereas the attempts beforehand were simply copy and pasted with not a care towards it. This isn't graded I'm purely trying to broaden my understanding so your effort will be greatly appreciated. Many thanks,
3) Give an example of a function f(z) which has the following properties. Justify your answer. a) A pole of order 3 at Zo= zi with residue & b) A simple pole at Zo-i-3 with residue Sli-3), and an essential singularity at Z₁ = i with residue 6. c) A pole of order 4 at Zo= 4; -1 with residue 5, and a simple pole at Z₁ = -i with residue -/-/- 2. 1.-3. 4) Let the curve C be given by the graph of the function y= f(x) with f(x) = coshx, a) Draw a sketch of the curve b) Give a path 8: [0,1] → [ which has the curve C as its image c) Compute the length L of the curve
Transcribed Image Text:3) Give an example of a function f(z) which has the following properties. Justify your answer. a) A pole of order 3 at Zo= zi with residue & b) A simple pole at Zo-i-3 with residue Sli-3), and an essential singularity at Z₁ = i with residue 6. c) A pole of order 4 at Zo= 4; -1 with residue 5, and a simple pole at Z₁ = -i with residue -/-/- 2. 1.-3. 4) Let the curve C be given by the graph of the function y= f(x) with f(x) = coshx, a) Draw a sketch of the curve b) Give a path 8: [0,1] → [ which has the curve C as its image c) Compute the length L of the curve
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