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- , Let f(x) = cos (2x²) - 1 x² -. Evaluate the 10th derivative of fat x = 0. f(¹0) (0) = Hint: Build a Maclaurin series for f(x) from the series for cos(x).The function f(x)=3xln(1+x) is represented as a power seriesUse the difference to find a power series representation for the function f(x)=3/(1+x)2.
- cos (6x2 Let f(x) 1 Evaluate the 10th derivative of f at x = 0. x2 f(10) (0) = Hint: Build a Maclaurin series for f(x) from the series for cos(æ).The function f (x) = 2x / 4-x expressed as a power series is:Let f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?