4(1). Find the Laurent series expansion for (22-1)(+2) in the annulus {1 < [z] <2}.
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- Find the fourth term of (3a22b)11 without fully expanding the binomial.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) + 18
- Find the Taylor series for f(x) centered at 5 if 8(n+4) fln)(5) = 4n n = 0Find 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) + 16
- Find the Laurent series expansion for f(z) = about z, =1 in the domain z-1 < 2. (z–1)(z–3)Use the binomial series to find a Taylor polynomial of degree 3 for T3(x) = ( ) + )x+ )x² + ) x³ 3 1 1+ 3xFind the Taylor series for f(x) = - centered at a = 2. (A) ED (-1)" 2n+1 (х — 2)" (В) У (-1)" (n+ 1) 2n +2 (-1)*+1 (п + 1) 2n +2 (x+ 2)" (C) (x – 2)" (D) (-1)" (n + 1) 2n +1 n=0 (x- 2)" n=0 n=0 n=0 (E) Σ (-1)" (х- 2)" (F) (-1)" +1 2" n=0 (x – 2)" (G) §(-1)*+1 (n + 1) (х — 2)" (Н) (х — 2)" (-1)" +1 2" n=0 2n +1 n=0 n=0
- Q7.4 Find the taylor series for fcx) = centered at a= 2 %3D (A) 1y"-1 (n+ 1) 22 00 (-1y+1 -(x-2)" 2 n=0 (x-2)" (B) n=0 (D) E 2-1 (x- 2) n=0 (-1)*-1 (-1)" (n + 1) (x – 2y" (F) 00 (E) (-1у (x- 2y? 2n-1 n=0 n=0 (G) E (-1)"- (n+ 1) (x - 2y 2-1 n=0 Chose 1 of the given options as your answer!4. a) Find an infinite series representation for / *-dx. Include at least the first four 1+x3 nonzero terms. b)를 Compute the second order Taylor polynomial at x = 2 of f (x) 4(6 + x)}. Determine whether the following series converges or diverges: E In=3 n In(n*) Determine whether the following series converges or diverges, and if it converges 2n+2 compute the sum: 2n=2 1Qen-2Obtain the Laurent's series expansion for (7z – 3) (z + 1)(z)(z – 3) in the region 1 < ]z + 1[ < 3.