Please Show your work Power Series: Find new from a known 1. Represent the funct

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Power Series: Find new from a known 1. Represent the function f(x) = 9/1-5x as a power series. 2. (a) Represent the function f(x) = 6/2+9x^2 as a power series. (b) What is the interval of convergence for the series from part (a)? (c) List the first three coefficients ao, a1, and a2 of the series from part (a). (d) Use the series from part a to find the power series for f(x) =6x^5/2+9x^2. (e) Use the series from part a to find the power series for f(x)=6/x^5(2+9x^2). 3. Represent the function 1(x) = ln(1 ? 9x) as a power series. (hint: derivative first) 1 4. Represent the function f(x) =1/(1+x^2) as a power series. (hint: integrate first)

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