15. Let f(x) = 3x2 -2x+5. Find the first-, second-. and third- order Taylor polynomials, P1 (x), P2(x), and P3(x), for f at 1. of Explain why f(x) = P2(x) = P3(x). 20. Use th 16. Let f(x) = 4x3 - 5x2 - 6x + 7. Find the first- through a Mac fourth-order Taylor polynomials, P, (x), P2(x), P3(x), and Macla P4(x), for f at 1. Explain why f(x) = P3(x) = P4(x). that f 17. Let f(x) = ax3 + bx2 + cr+d, where a, b, c, and d are con- have stants. Find the first- through fourth-order Taylor poly- nomials, P1 (x), P2(x), Pa(x), and P4(x), for f at xo. Explain why f (x) = P3(x) = PA(x). Skills In Exercises 21-30 find the fourth Maclaurin polynomial P4 (x) 49. cos for the specified function. 51. sin 21. cosx ex 53. In 23. sinx 24. In(1 + x) 55. co 25. cos 2x 26. sin 3x 1 +x Exercis 27. V1 - x 28. 1 - x Examp 29. xsinx 30. x2ex the Ma In Exercises 31-40 find the Maclaurin series for the speci- 57. Sh fied function. Note: These are the same functions as in Ex- se ercises 21-30. 58. SH 31. cosx 32. ex rie of 33. sinx 34. In(1 + x) Si 35. cos 2x 36. sin 3x 59. 37. V1 - x 1+x 38. 1 - x 61. 39. xsinx 40. x2ex In Exercises 41-48 find the fourth Taylor polynomial P4(x) for 63. the specified function and the given value of xo. 41. Cosx, 2 42. ex, 1