(18) a) Using the Maclaurin series for f(x) = e* find a power series representation for g(x)= –x² b) The generalized normal distribution function 0(z)= e 2 dx calculates the probability 2л that a standard normal variant assumes a value in the interval [0,z]. Use at least four terms from your series in a) to approximate the probability that a standard normal variant will fall in the interval [0,1].

Q: Represent the function 4 In(5 – x) as a power series (Maclaurin series) 00 E enx" n=0

A: Introduction: The formula for the Maclaurin power series of the function f(x) is given by,…

Q: Nhich of the following p-series are divergent? 00 ロと-4 S ロEsk-品 Σ 6666 10000 k38 ロと-7 1 k=7 ロEk…

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Q: Find a power series representation for f(x) = In(1 + 3x) by integrating the power series for f' (x)…

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Q: (x-7)" Find the radius and interval of convergence for the power series Ln=0 n+1 100 O R.O.C=1,…

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Q: Use the Maclaurin Series for sine and cosine to find first four terms for nonzero f(x) = tanx

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Q: Determine the Maclaurin series for f(x)=√1+x.

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Q: Use multiplication of power series to find the first four nonzero terms in the Maclaurin series for…

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Q: Which is the power series representation (a) n! n=0 (b) -1)". (2n)! n=0 2n+1 (c) X-1)* (2n + 1)! n=0…

A: We have t

Q: Explain the relationship between power series and the Laplace transform

A: To state relation between power series and Laplace transformation.

Q: Represent the function 4 In(10 – x) as a power series (Maclaurin series) ( f(x) = >, n=0 CO Ci = C3…

A: We have to solve given problem:

Q: Define a power series  f(x)=Σn≥0(anxn)=x+x2+2x3+3x4+5x5+8x6.

A: We have to solve given problem: