Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. 1 = (x)6 (1+13x?)? using f(x) 1+ 13x

How many nonzero terms of the Maclaurin series for ln(1 + x) do you need to use to estimate ln(1.2) to within 0.000001?

Give a power series representation for the following. x/1+x^4

3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. x" п3 x" (c) n23n (a) x" (b) n=1 n=1 n=1