Can you please help me with 23 and 56? Thanks so much!

In Exercises 3-18, find the Maclaurin series and find the interval on which the expansion is valid. 3. f(x ) = for |x 1 + 10x 4. f ( x ) = - 1- x3 Exerc 5. f (x ) = cos 3x 6. f(x) = sin(2x) 44. I 7. f(x) = sin(x2) 8. f (x ) = efx rin se 9. f(x) = In(1 -x2) 10. f (x) = (1 - x)-1/2 45. for | 11. f(x) = tan-1(x2) 12. f (x ) = x2ex2 13. f (x ) = ex-2 1 - cos x 14. f (x ) = X 46. 15. f(x) = In(1 - 5x) 16. f(x) = (x2+2x)ex prox 17. f(x) = sinh x 18. f(x) = cosh x 47. need In Exercises 19-30, find the terms through degree 4 of the Maclaurin se- com ries of f(x). Use multiplication and substitution as necessary. 48. 19. f(x) = e* sin x 20. f(x) = et In(1 -x) R > Q sin x toniabagg mat a do 1 1 21. f(x) = 1 - x 22. f (x) = - COI 1 + sin x of mainder 23. f (x ) = (1+x) 1/4 24. f (x) = (1+x)-3/2 49 F( 25. f(x) = ex tan- x ich that 26. f(x) = sin (x3 - x) (a) es on li 27. f(x) = esinx 28. f ( x ) = elet ) the (b) IT sene 29. f (x ) = cosh (x2) 30. f(x) = sinh(x) cosh(x) CO ication In Exercises 31-40, find the Taylor series centered at c and the interval on which the expansion is valid. 31. f (x ) =-, c=1 X 32. f(x) = e3x, c=-1 33. f(x) = 1 - x C = 5 34. f(x) = sinx, c = 35. f(x)614 CHAPTER 10 INFINITE SERIES 7 In Exercises 51-54, express the definite integral as an infinite series and R find its value to within an error of at most 10-4. 51 . cos ( * 2 ) dx 52. tan -' (x2) dx 53 . fe-x 3 dx 54. dx Ex Vx 4 + 1 74 In Exercises 55-58, express the integral as an infinite series. to 1 - cost t - sint 55 -dt, for all x 56. dt, for all x t 57 . In ( 1 + 1 2 ) dt , for lx ) (-1)"27 x? 76. n=0 seri 60. Which function has the following Maclaurin series? 77 . (- 1 )k rin s 3 k+ 1 ( x - 3 ) k 1 5 K = 0 78. For which values of x is the expansion valid? 79. 61. Using Maclaurin series, determine to exactly what value the following series converges: X = 80. n=0 ( 2n ) ! f ( x ) 81. 62. Using Maclaurin series, determine to exactly what value the following series converges: (a) U