Calculus 2: Taylor and Maclaurin seriesPlease help solve 1-10. Please show your work.(Answers are given at the bottom of the picture)

In #1-5, find the Maclaurin series for the function. 1. f(x) = (1-2)-2 4. f(x) = r COS 2. f(x) = re- *3. f(x) = (1 -2)/3 *5. f(x) = - V4+ 12 In #6-8, find the Taylor series for the function centered at the given value of a. 6. f(x) = =, a =-3 8. f(x) = a =9 *7. f(x) = sinx, a= 9. Use the Maclaurin series for sin ar to approximate sin 30 with error less than 5 x 10-6. *10. Use series to approximate Vi+ r dx with error less than 5 x 10-6. Final Answers nan-1 n=1 DO (-1)"an+1 2. 1=0 n! *3. 1 - 1 . 4 . 7 . ... . (3n - 5) 7 =2 3" n! DO 4. ) (-1)" cintl 22n (2n)! #5. 1 52+) (-1)"1 . 3 . 5 .... . (2n - 1) 2n+1 n= 1 n! 23n+1 6. (2+3)" 32+1 n=0 *7. (-1)" n=0 (2n)! (2 - 7/2) 2n 8. (-1)"1 . 3 .5 .... . (2n - 1) n=1 2n 32n+1 n! 2(x -9)" 9. 0.05233 *10. 0.40102