Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 15x cos(x2) Step 1 We are asked to find the Maclaurin series for a function involving cos(x). Recall the Maclaurin series for cos(x). cos(x) = (-1)" x 2n ( 2n ) ! The same equality would be true for any variable, and in particular for u = 1x2. 14 Therefore, the Maclaurin series for cos(_1 x2) is n 2 5 ( - 1 ) 7 14 S(-1)' n = 0 D= 0 (14 ) 2n (20)!' 142n (2n)! Step 2 We have found the following Maclaurin series. cos (x2 ) = (-1)"- x 4n n = 0 14 2n ( 2n ) ! Now we can use this to find the Maclaurin series of the given function, treating the term 15x as a constant and using the rule Ecan = cCan f(x) = 15x cos _1 x2 = 15x \\ (-1)" - x 40 n = 0 1420 (2n)! (-1)"(x2n+ 1 (14) 2 (2n)! XUse a Maclaurin series in this table to obtain the Maclaurin series for the given function. x} = 3 sin2(x) [Hint Use sin2(x] = %(1 cos(2x]) 2n+1 I Z( (1)\" m ) 8 Need Help