Derive sinh (a + Bi)x cosh (a + Bi)x In form of Power Series Expansion.

Using f (x) = In(3 – 2x), list the Maclaurin series expansion %3| (e.g., f(O)x, f(1)x, f (2) x, f(1)x and f ®(0), f(1)(0), f(?) (0), f(n) (0))

Discuss the idea of power series method and prove that y`=2xy

I think this is Taylor series, why there is no ! mark, and what does O(x^3) mean? Continuing expansion? Nonlinear dynamic, Bifurcations

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plz solve it within 30-40 mins I'll give you multiple upvote

Laurent Series of Q30Find the fiz 3 (Z-1)2 (Z-3) C:/Z/=1

How do I solve this question

Lion Use the power series f(x) = Select one: O a. O 4 (4x + 1)² C. 8 O b. Σ (4)" ·n.x² − 1 n=0 1+x d dx - n=0 Σ(-4)" ·n-x²-1 d. Ž (4)".x" n = 0 Σ(-4)" · (n − 1) x²-1 n=0 Time left 1:2 Σ(-1)"x" to determine a power series centered at 0 for the function x ○ e. Ž (-4)”.x² n=0 n=0 4x+1

Approximating the sum of an alternating series. If the alternating series (-1)"+'bn satisfies the requirements for the alternating series test, 1. b, > 0 for all n 2. b, 2 bn41 for all n > N where N is an integer 3. b, →0 s n → 00 Then, for n > N, S, =E(-1)*+1bx = b1 – b2 + bz – b4 +...+(-1)"+lb k1 approximates the sum of the series, S, such that |S – S,| < ba+1- In other words, the size of the approximation error is smaller than the n + 1st term, b41 How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (-1)7+1 error < 0.005 n=1 terms are needed.