polynomial approximation. Calculate the error of each app 6 Exercise. Derive the closed formula for the Maclaurin series representation of the function, h(x ) = sin2 x . Hint: You may find the trigonometric identity cos(2x) = cos (x) - sin(a), to be useful. 7 Exercise. Determine the radius of convergence for the power series from #6.2! 3! 4! 5! n! 73 sin x = x Is + (- 1)~ x 2n+ 1 + 3! 5! 9 ! + 7! + . . (2n + 1)! 7 2 cos x = 1 - (- 1)2 x 2n . 2! 4! 6! 8 ! . + +.. (2n)! 7 3 .9 ( - 1 ) ~ x 2n+ 1 arctan x = x + . 3 2n + 1@ h ( x ) = = sina x 2 ( sin 2 x ) = (1 - cos ( 2 x ) 1= 1- cos ( 2x ) - Cos ( 2x ) 4 4 from power series table on p 674 : COS X = 2 ( - 1)n x an ( 2n ) ! CoS ( 2x) = = ( - 1)" 2 an ( 2n ) ! cos ( 2X) ( - 1 ) 2 x 2h 4 r= 1 4 ( 2n ) ! - - Cos ( 2x ) - - ( - 1 ) - 2 x an ( 2n ) . - ( -1) 2 x 4 h = 1 4 ( 2 n ) ! - = 4 ( 2n )