Help with all plz

1 . Find a power series representation for the function. [ ( x ) = 9 X =0 1-x2 /t (x ) = 21 2 , detamine the interval 2 : Find power series representation for the function. fu ) = x - 1 determine interral. X + 6 3 . use a power series to approximate the definite integral to 6 decimal places fox In ( 1 + * 3 ) dx 4 : use the definition of a Taylor series to find First four nonzero term of sevies fo fix ) centerat at given value of 9 F (x) = 4 cos ? ( x ) a zo 5. Find the Maclaurin Series for [(x) using Maclaudin series. don't show that RuckI to f(x) = 6x 4 _ 5x2 +5 $ find the associated radius of R 6 : Find the Taylor series for fix) centered at given value of a f (x ) = exx , a = 3 F ( 1 = 2 7 8 R = 0 radius of convergence 7 : use binomial series to expand the function as power series 9 & state the radius of convergence . (6+ x ) 3 8 : Evaluate the indefinite integral as an infinite series [arctan( x 4 ) dix 9: Find the sum of series 2 n=0 5hni