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4. 5. Find power series representations for the functions below. Include their intervals of convergence: _ b) h(x) Consider a function f that has a power series expansion at a. f (x) = co + Cl(x a) + C2(x + C3(x + Assume we have the equation for f (in short form) but we do not know any of its power series representations. We need a wayto figure out the values of the coefficients. Use the following steps to derive the Taylor series of the function f at a. a) b) c) d) e) Write the general form of the power series as shown above. Write the first four derivatives of f with respect to x. Find expressions for f and f Use these results to derive formulas for the coefficients co, Cl, c2, c3, . Substitute the appropriate formula for each coefficient in the original power series. This gives you the Taylor series. Write out the Taylor series of f for the special case in which a = O. This result is known as the Maclaurin series.