Match each function with its power series representation. Functions: Power Series: Function 1: 2 1 f(x) = 2+ 7x Power series (29): 247 for lel < n=0 Function 2: Power series (13): g(x) = xe. El-1)" (; Power series (83): Function 3: 1 h(x) = r*e=*, E(-1)"; n+1 n=0 Power series (37): Function 4: 1 E(-1)"; p(x) = a² In(1 + x*) for |æ| < 1. 2n +1 Power series (7): 3" Function 5: n! q(x) = Vr tan¬(VT) for |x| < 1.

Q: Start with the geometric series (a) Find the sum of the series 00 (i) Σ nx", |x| < 1 n = 1 (ii) SW n…

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Q: O Let f (x) be a function which is represented by the power series f(x) =E(-1)"-1)". n3 What is the…

A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

Q: Give the first four nonzero terms of the series about x = 625 representing the function f(x) = v

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Q: If f(x) = = ∞ n=0 n ∞ -2” and g(x) = Ỹ ( − 1)" mæª, find the power series of(f(x) – g(x)). n n=0 Σ…

A: The objective of the question is evaluate the sum of two series.

Q: Find a formula for the power series of f(x) = 2 ln (1 + x), −1 < x < 1 in the form Σ an. n=1 2 1 + x…

A: Given function is ,               f(x) = 2 ln(1+x)  Power series :  Power series of a function…

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: If f(x) = 2x" and g(x) Σ na", find the power series of f(r)g(x). %3D n=0 00

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Q: rewrite the function as an expression which includes the sum of a power series B: modify your…

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Q: 5. Consider the function f(x) = r tan-(") (a) Find a power series representation for the function.…

A: series and sequences

Q: Find the power

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Q: Rewrite -ln(3)+ln(4)-ln(5)+...+ln(20) using summation notation.

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