1) Use the binomial series to expand the function as a power series. Compute the following coefficients: 2) Find the first four (zero or nonzero) terms of the Taylor series for the function about the point . term 0 = term 1 = term 2 = term 3 = 3) The function has a Taylor series at . Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms. 4)The function has a Taylor series at . Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms. 5) By recognizing each series below as a Taylor series evaluated at a particular value of , find the sum of each convergent series. A. B. Note: You can earn partial credit on this problem. 6) Find the sum of the series 7) Use a Maclaurin series derived in the text to derive the Maclaurin series for the function . Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms. 8) Suppose that you are told that the Taylor series of about is Find each of the following: Hint: Do not try to compute the derivatives directly using the porduct rule. Instead, use the fact that the coefficient of in a Taylor series is .