Ranking Taylor Series Error Bounds

Question

The table below provides four Taylor polynomial approximations for $$\sin(0.5)$$ and their corresponding error bounds. For the alternating series for sine, the approximation error is bounded by the absolute value of the first omitted term. Which of the following correctly lists the approximations in order from largest error to smallest error?

| Label | Degree of Taylor Polynomial | Error Bound            |
|-------|-----------------------------|------------------------|
| A     | 1                           | $$\frac{0.5^3}{3!}$$    |
| B     | 3                           | $$\frac{0.5^5}{5!}$$    |
| C     | 5                           | $$\frac{0.5^7}{7!}$$    |
| D     | 7                           | $$\frac{0.5^9}{9!}$$    |

Accepted Answer

A, B, C, D

Answer

B, A, C, D

Answer

D, C, B, A

Answer

A, C, B, D

Label	Degree of Taylor Polynomial	Error Bound
A	1	$$\frac{0.5^3}{3!}$$
B	3	$$\frac{0.5^5}{5!}$$
C	5	$$\frac{0.5^7}{7!}$$
D	7	$$\frac{0.5^9}{9!}$$

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