Math 2414 Name: Taylor Series 1. Use the definition of Taylor series to find the Taylor series centered at 3 for the function f(2) = 2. Use the definition of Taylor series to find the Taylor series centered at [ for the function f(x) = sin x.3. Use elementary Maclaurin series to find the exact sum of the following series. (a) (-1)"(In 2) 12 (b ) ( - 1 ) n - 1 72=0 n! n = 1 n 4n 4. Use elementary Maclaurin series to find the exact value of the following limits. (a) lim tan x - T (b) lim x sin (1) 1 -7 00