Question

Reply to the following Discussion Question with a substantive post - one that demonstrates that you understand the mathematical concepts and provides an explanation rather than just making a simple statement about the topic: Decide if the statement is true or false. Assume the Taylor series for a function converges to that function. Given an explanation for your answer. The Taylor series for sin x about x = h is (x-7)3 (x – T) (x-7 + 7) 3! 5!

Answer 1

a function song an around The Taylor series expansion of point (let say 'a'), is approximation of that function around the point Ton the is given region, in which function And the formula for this analytic. by- = f(x) = f(a) + (x-a) f'(a) + (x-2) f" (P) + (2-a) th (9) n! antire function. So, around Since sinx is an x= π, sinx : fim) + (x-1)} (M) + (2-13'4" (1) 2! abone values - calculate the Now we sin T Cosx f'(a) = f(t) = f'(T) = cos (1) = -1 - F"(x) = sinx, f"(= -sin (1) = f(x) = f" () = -cos (T) = 1 1 By eqn 0 - (x-11) (-1) + (x sinx = ot + (x-rijs - (x-T) + (x-T, 3 sinx = 3!