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Find the Taylor polynomials up to degree 6 for f(x) = cos x centered at a = 0.?
I feel like I am getting the right answer, but I may be submitting it in a wrong format on WebAssign.
2 Answers
- Elizabeth MLv 79 years agoFavorite Answer
This is a standard series, cosx= 1 -x^2/2! + x^4/4! -x^6/6! to degree 6=1-x^2/2+x^4/24-x^6/720
To obtain it you use the fact that f(x)=f(0) + (x/1!)f'(0)+(x^2/2!)f"(0)+(x^3/3!)f"'(0) +...+(x^6/6!)f^(6)(0)
which should give the same answer. Note that the odd powers will be associated with sinx
and since sin0=0 these will be zero so you only get even powers of x.
