Question: Consider the function f(x)=3tan-1(x2).a. Differentiate the Taylor series centered at 0 for f(x).b. Identify the function represented by the differentiated series.c. Give the interval of

Consider the function f(x)=3tan-1(x2).a. Differentiate the Taylor series centered at 0 for f(x).b. Identify the function represented by the differentiated series.c. Give the interval of convergence of the power series for the derivative.a. Choose the correct answer.A.3x2x63x1053x147 cdotsB.6x-6x56x9-6x13 cdotsc.3x2-x63x105-3x147 cdotsD.-6x6x5-6x96x13-cdotsb. The differentiated series converges to (Type an expression using x as the variable.)c. The interval of convergence for the differentiated series is

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