(a) (5 points) Write out the 6th order Taylor approximation to f(x) = cos(x) centered at a = 0. (b) (5 points) Write out

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A 5 Points Write Out The 6th Order Taylor Approximation To F X Cos X Centered At A 0 B 5 Points Write Out 1 (28.07 KiB) Viewed 32 times

(a) (5 points) Write out the 6th order Taylor approximation to f(x) = cos(x) centered at a = 0. (b) (5 points) Write out the remainder term for the Taylor approximation in part (a). (c) (10 points) Explain why in general, the remainder term for the n-th order Taylor approximation to cos(x) centered at 0 has absolute value less than or equal to |z|n+1 (n+1)! (d) (5 points) Use (c) to argue the radius of convergence of the Taylor series for f(x) = cos(x) centered at a 0 is infinite.