Let f(z) = ((z – 3i)² + 9)ez- The Laurent series representation of f(z) in the domain 0 < |z – 3i| < ∞. (+r aE 1 a) (z – 3i)² + (z – 3i) + En=0 n=0\(n+2)! | n!) (z-3i)" 1 1 b) 2(z – 3i) + E-0 1=0 n! (z-3i)" c) 9 + 9(z – 3i) + En=2 (n-2)! + (z – 31)" 1 а. O b. С.
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- Find the Taylor series for f(x) centered at the given value of a. f (2) = x* – 5x2 +1, a = 2 f(n) (2) (г — 2)" — 3-12 (r — 2)+19 (т — 2)? +8 (г — 2)8 + (г — 2)" n! O n=0 f(m) (2) (r – 2)" = 3+12 (x – 2)+19 (x – 2)² –8 (x – 2)* +(x – 2)4 - n! O n=0 f(m) (2) (x – 2)" = -3+12 (x – 2)+8 (x – 2)²+19(x – 2)³+(x – 2)4 n! O n=0 f(m) (2) (r – 2)" = -3+12 (x – 2)+19 (r – 2)²+8(r – 2)°+(x – 2)* n! O n=0 f(m) (2) (г — 2)" — — 3+12 (г — 2)—8 (т — 2)2+19 (т — 2)8— (х — 2)4 n! n=0 Need Help? Read It 8W! W! W! W! W!A periodic function is defined as follows: (3 for-1 ≤ t < 0 16 for 0 ≤t<1 f(t) = {2 where f (t + 2) = f(t). Find the first four non-zero coefficients for the Fourier series expansion.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 = -1Let 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 -πFind the Fourier series expansion of In(3 – x) around 1. Oa. x - 1 (x – 1)² (x – 1)³ In(2) + ... 8 24 Ob. x –1 (x – 1)² (x – 1)³ In(2) | 8 24 x- 1 In(2) – (x – 1)2 (x – 1)³ | 4 d. X-1 (x – 1)2 (x – 1)³ In(2) + 2 ... 4 3. 3. 2] 2. 2.Given 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:1)Determine S[f] (Fourier series) if: d) f(x)=ex+x ,x∈ [-1, 1] such that f(x) = f(x + 2)Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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