1. [-/2 Points] DETAILS SCALC8 11.10.011.MI. MY NOTES Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R,(x) -> 0.] f ( x) = 7(1 - x) -2 F(X ) = ) n = 0 Find the associated radius of convergence R. R : 2. [-/2 Points] DETAILS SCALC8 11.10.012. MY NOTES Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that R,(x) - 0.] f(x) = In(1 + 3x) F(x) = C n = 1 Find the associated radius of convergence R. R = 3. [-/2 Points] DETAILS SCALC8 11.10.022.MI. MY NOTES Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R,(x) - 0.] f(x) = 6/x, a = -4 f(x) = > n =0 Find the associated radius of convergence R. R=4. [-/2 Points] DETAILS SCALC8 11.10.504.XP.MI. MY NOTES Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R,(x) - 0.] f(x) = 2 cos(x), a = 5n f (x) = ) n = 0 Find the associated radius of convergence R. R : 5. [-/1 Points] DETAILS SCALC8 11.10.507.XP. MY NOTES Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 2 cos Ix n = 0 6. [-/1 Points] DETAILS SCALC8 11.10.509.XP. MY NOTES Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = esx + 2e-5x 1= 07. [-/1 Points] DETAILS SCALC8 11.10.510.XP.MI. MY NOTES Evaluate the indefinite integral as an infinite series. e - 1 dx + c 8. [-/1 Points] DETAILS SCALC8 11.10.056. MY NOTES Evaluate the indefinite integral as an infinite series. arctan ( *5) dx E () +c 9. [-/1 Points] DETAILS SCALC8 11.10.062. MY NOTES Use series to evaluate the limit. 1 - cos(5x) x - 0 1 + 5x - e5x10. [-/1 Points] DETAILS SCALC8 11.10.074.MI. MY N Find the sum of the series. (-1)" x 20 n = 0 4 (2n)! 11. [-/1 Points] DETAILS SCALC8 11.10.076. MY Find the sum of the series. n = 0 2"n! 12. [-/1 Points] DETAILS SCALC8 11.10.078. MY Find the sum of the series S. 2 - 2 In(5 ) + 2 (In (5))2 _ 2 ( In(5) )5 +... 2! 3 ! S =Find the Taylor polynomial 73(x) for the function f centered at the number a. f ( x) = _, a = 4 73(X) = Graph f and 73 on the same screen. 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 T3 T3 TTTTTT O 1 2 3 4 5 6 7 O 1 2 3 4 5 6 7 2.0/ 2.0 1.5 1.5 1.0 1.0 T3 0.5 0.5 T3 O 1 2 3 4 5 6 O 1 2 3 4 5 6 7Find the Taylor polynomial 73(x) for the function f centered at the number a. f(x) = xe-8X, a =0 T3 (x) = Graph f and T3 on the same screen. 4 2 N 4 1 1 -1.0 -0.5 X 0.5 1.0 -1.0 -0.5 X 0.5 1.0 -1- -1- - 2 -2 -3 - 3 O O N 4 1 1 -1.0 -0.5 X 0.5 1.0 -1.0 -0.5 X 0.5 1.0 -1 -1 -2 -2 -3 -3 O O