4(1). Find the Laurent series expansion for (22-1)(+2) in the annulus {1 < [z] <2}.
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- 4a) What is the Taylor series of the function 3x5 2x4 + 15x3 + 13x² 12x – 5 at the point c = 2?Find the Taylor series generated by f at x = a. f(x) = x 2- 4x + 3, a = -3 (x + 3)2 - 10(x + 3) + 18 (x + 3)2 - 10(x + 3) + 24 (x- 3)2 -10(x- 3) + 24 O (x- 3)2 - 10(x - 3) + 18Find the Taylor series of the cubic function ³ about x = 2. 12(x - 2)² 6(x - 2)³ + 2! 3! 12 (x-2) + 1+ I x² 2 8 8+ 12 (x-2) + 6(x - 2)² + (x − 2)³.
- Find the Taylor Series of the following: a. f(x) = e¯6x about x = -4 b. f(x) = In(3+4x) about x = 0 7 c. f(x) = – about x = -3 x4 d. f(x) = 7x² – 6x + 1 about x = 2 е. f(x) — - 1 about x = -2 (4+9x)² f. f(x) = x³ – 10x² + 6 at x = 3 -3 find laurent series for function f(z) in this set of numbers M(0; 3; 4) if f(z) = (2*j)/((z-3)(z-4))Find the Taylor series for f(x) centered at 5 if 8(n+4) fln)(5) = 4n n = 0
- Find the Taylor Series for the following functions:Find the Taylor series generated by f at x = a. f(x) = x3 + 8x2 + 7x + 6, a = -2 O (x + 2)3 - 2(x + 2)2 - 13(x + 2) - 16 O (x + 2)3 - 2(x + 2)2 - 27(x + 2) - 16 O (x + 2)3 + 2(x + 2)2 - 27(x + 2) + 16 O (x + 2)3 + 2(x + 2)2 - 13(x + 2) + 16Find the Laurent series expansion for f(z) = about z, =1 in the domain z-1 < 2. (z–1)(z–3)