Let f(z) = ((z -3i)² + 9)ez-31 The Laurent series representation of f(z) in the domain 0 < |z-3i| <∞o. a) (z − 3i)² + (z − 3i) + Σn=0((n+2)! + i)(z-31)² 1 1 b) 2(z-3i) + En=0; n! (z-31)n c) 9 + 9(z-3i) + Σn=2((n-2)! 2 ((1²2): + 2²/1) (2 − 3i)* O a. O b. O C.
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![Exercise 11. *
Let f(z) = ((z – 3i)² + 9)ez-si
The Laurent series representation of f(z) in the domain 0 < ]z – 3i| < o.
a) (z – 3i)2 + (z – 3i) + Ln=0Cn+2)!
1
+
n!) (z-3i)"
1
1
1
b) 2(z – 3i) + En=o;
100
n! (z-3i)n
)(= - 30)"
1
c) 9 + 9(z – 3i) + E=2
а.
O b.
O c.
a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc47fdc0-9c50-4344-8904-63924b17ea71%2F58e82859-288a-448c-b079-befb353b3ade%2Ff76i7d_processed.jpeg&w=3840&q=75)
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- Find the Taylor series for f(x) centered at the given value of a. f (x) = x* – 312 +1, a = 2 f(m) (2) (x – 2)" = -5–20 (z – 2)+21 (x – 2)² +8(x – 2)³+(x – 2)* n! 0 f(n) (2) (x – 2)" = 5+20 (x – 2) +8 (x – 2)² +21 (x – 2)* +(x – 2)* n! 0 f(n) (2) (r – 2)" = -5+20 (x – 2)+21 (z – 2)² –8 (x – 2)°+(x – 2)* %3D n! f(n) (2) Σ - (x – 2)" = 5+20 (x – 2)– 8 (r – 2)² +21 (x - 2)° –(x – 2)“ n! 0 f(m) (2) (x – 2)" = 5+20 (x – 2)+21 (z – 2)° +8 (x – 2)* +(x – 2)* n!Determine the Fourier Series of: f(t) = { { Α= A f® = ΣΑ#t-1)*+1 + B]D(nat) f(t) n=C Β = C = -3, 3, D = -1Determine the nth partial sum of the Fourier Series of: + x, - T < x < 0 f(x) = х, 2 0A periodic function, f(x) with period 4x is defined as - 2n sx<-1 - nSX<0 2n, %3D f(x) Osx<* 2n, Sketch the graph of f(x) on the interval [-5x, 57). Determine if f(x) is an even, odd or neither even nor odd function. a) b) Find the Fourier series of f(x).4. a) Show that exp(z) in the range 0< < is represented by the Fourier series 2 sin(2) 4 sin(4r) 6 sin(6z) exp(z) - exp (т)) 17 37 3 sin(3z) sin(x) +((1+ exp(7)) 2 10Let f(z) = ((z – 3i)² + 9)ez The Laurent series representation of f(z) in the domain 0 < ]z – 3i| < o. 1 a) (z – 3i)2 + (z – 3i) + E-o (n+2)! n!) (z-3i)n 1 b) 2(z – 3i) + Ln=0n! (z-3i)" 1 00 c) 9+ 9(z – 3i) + E-2 +) (z –: ;+)(z - 31)" 100 (п-2)! а. O b. О с.Q) find Fourier series on [-7,1] – 1 |4 -πGiven the formula y(s + h) – 2y(s) + y(s – h) +y(")hP + O(h9) y"(8) h2 use the Taylor series h? h" y(s +h) = y(s) + hy'(s) + -y"(s) + ...+ 2! Ty(n)(s) + O(hn+1) n! to determine the integer values of c,p, q and r. (Note that integer values can be positive, negative or zero. Do not forget to include the minus sign for any negative values.) Enter c: Enter p: Enter q: Enter r:Find the Taylor's or Laurent's series expansion of the complex variable function which is represented by : f(z) = ; i) 1< ]z] < 2 ii) ]z|< 2. Also (z²–1)(z²+4) z2 classify the singularity of f(z) %3D (z-2)ez-1Determine the Taylor series generated by the function f (x) 1 about the point a = 2. x + 3 5(-1)"(x – 2)" 5n+1 n=0 5 (-1)"(x – 2)" 3n+1 n=0 5 (x – 2)" Σ 5"+1 n=0 (– 1)"x" 5n+1 n=0 IIRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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