Use taylor's THeorem to determine the accuracy of the approximation: cos(.3) ~=1 - (.3)^2 / 2! + (.3)^4 / 4! when i use taylors theorem, i use (.3)^4 / 4! which gets me 2.03e-10 but the asnwer is R<=2.03e-5
The error does NOT involve f^(n+1)(c). It involves f^(n+1)(x) for some number between 0 and c (here .3). Since you don't know that number, you use the largest possible value of f^(n+1)(x) between 0 and c to get an upper bound on the error. Since cosine is decreasing, its largest value is cos(0)= 1.