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- Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1 a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1 b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1 c. Determine the interval of convergence for the series given in (b). d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.(5) Find the first 5 terms (a quartic polynomial) of the Taylor series for f(x) = 10ª.(1) Find the Taylor series of f(x) 1 centered at I = 0. You can use power 5 - I series properties or directly derive the Taylor series for this function.