Home
Answered Questions
Advanced Math
(12 Points) In The Taylor Series Approximation Of A Function For Value X Approximated At Point A, Th

(12 points) In the Taylor series approximation of a function for value x approximated at point a, the terms are as follows. Term 0 = f(a) Term n == "")(x - 2)", where f(n) is the nth derivative off. We will call s(n) the approximation derived by the sum of the terms 0 through n. The best way to get an approximation that converges quickly is if |x-al < 1. As we saw in class the easiest values to plug in for a when approximating sine or cosine are the numbers 12 tk, one of which will be less than 1 away from any real number chosen. For the following values of x, we will approximate cos x, finding the closest integer multiple of 12t, the approximation s(7) written to nine places after the decimal and the base ten exponent of the error cos(x) -s(7). x = 2 Closest integer multiple of 1211 = _ s(7) = base 10 exponent of the error cos(2) -s(7) = x = 4 Closest integer multiple of 421 = _ . s(7) = base 10 exponent of the error cos(4) -s(7) = x = 6 Closest integer multiple of 4210 = s(7) = base 10 exponent of the error cos(6) -s(7)=- x = 8 Closest integer multiple of 1211 = _ s(7) = base 10 exponent of the error cos(8) -s(7) =