Solve the problem.
-Find the Taylor series at 0 for g(x) = cos x (while evaluating cannot be directly applied, other techniques can be used to show that the Taylor series at 0 for g(x) = cos x converges for all values of x).

Question

Solve the problem.
-Find the Taylor series at 0 for g(x) = cos x (while evaluating  cannot be directly applied, other techniques can be used to show that the Taylor series at 0 for g(x) = cos x converges for all values of x).

Quizplus · Accepted Answer

The Taylor series for cos x at 0 is: 
cos x = sum((-1)^n x^(2n))/(2n)!
This series converges for all values of x. This can be shown using the alternating series test, which states that if a series has alternating terms that decrease in absolute value and eventually converge to 0, then the series converges. In the case of the Taylor series for cos x, the terms alternate in sign and decrease in absolute value, since factorial terms grow very quickly. Therefore, the series converges for all x. The correct choice is B.

Solve the Problem. -Find the Taylor Series at 0 for G(x) = Cos