If \[ I = \int_0^{2\pi} \frac{d\theta}{1 - 2p \cos \theta + p^2} \]show that if \( z = e^{i\theta} \)\[ I \] may be written as \[ \oint \frac{dz}{(1 - pz)(z - p)} \]Evaluate \( I \) using the Residue Theorem.

Let the given integral is --------- (1) For evaluate the above integral consider the…

Answered: If I = may be Evaluate I 20 do 1-2p000…

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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Untitled -> Q1: The following equation a=2.34+½2.7(5.9²-2.4?)+9.8log85 can be solved by Matlab program as a=2.34+1/2*2.7*(5.9^2-2.4^2)+9.8log10(85) 1-yes 2-no Q2: The following equation A=2sin½(a+b) cos(a-b) can be solved by Matlab program as A=2*sin(1/2*(a+b))*cos(1/2)*(a-b) 1-yes 2-no Q3: what the run of this command >> a=12,b=4;c=(a-b)+40-a/b*10 Q4: By hand (pencil and paper) write what will displayed if the following commands are executed in Matlab v=[35 46 78 23 5 14 81 3 55]; v(5:8)=[ ]; v(6)=90 Q5: By hand (pencil and paper) write what will displayed if the following commands are executed in Matlab A=[3 8 1 24]; B=4:3:16; K=[A';B'] Q6: Write a program in Matlab language to solve these equations: 4x-2y+6z=8 2x+8y+2z=4 6x+10y+3z=0 Q7: By hand (pencil and paper) write what will displayed if the following commands are executed in Matlab p=1:3:34; M=reshape(p,3,4); M(2,:)=[ ]; M(:,3)=[ ]; N=ones(size(M)) II
(ii) Prove that between any two zeroes of Inx lie one and only one zero of Jn+1x as well as In-1x.
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12:41 2) How many roots does the polynomial have ? a) 2x' - 4x? + 9x - 1 b) 2x - 9x - 1 1 3 4 5
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Find a polynomial of degree 3 that has zeros – 1, – , and 2 such that the coefficents are integers. 2' -
Find the minimal polynomial satisfied by √2 + √5. over Q.
Q.1) Find the product and simplity it possil ((r-q)^(2))/(5r+5q)*(5r)/(r^(2)-rq)
7. Let z be a root of the polynomial p(z) = (z + 1)" + z". Show that 1 Re z
3. What is the degree of the polynomial? * 6x² +2-7x + x' - x 4 O 1 O 2 4 O 10
19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1 + 6i)] - |

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If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the Residue theorem