Question

(a) Find lim_{x ? 0} (1 - cos x) / x^2. (b) Use your answer to part (a) to derive the approximation cos x ? 1 - 1/2 x^2 for x near 0. For x ? 0. (1 - cos x) / x^2 ? 1 - cos x ? cos x ? 1 - (c) Use your answer to part (b) to approximate cos(0.06). (d) Use a calculator to approximate cos(0.06) to four decimal places. Compare the result with part (c). The result from part (c) is the same to four decimal places. The result from part (c) is not the same to four decimal places.

          (a) Find lim_{x ? 0} (1 - cos x) / x^2.

(b) Use your answer to part (a) to derive the approximation cos x ? 1 - 1/2 x^2 for x near 0.
For x ? 0.
(1 - cos x) / x^2 ?
1 - cos x ?
cos x ? 1 -

(c) Use your answer to part (b) to approximate cos(0.06).

(d) Use a calculator to approximate cos(0.06) to four decimal places.

Compare the result with part (c).
The result from part (c) is the same to four decimal places.
The result from part (c) is not the same to four decimal places.

(a) Find limx ? 0 (1 - cos x) / x^2.

(b) Use your answer to part (a) to derive the approximation cos x ? 1 - 1/2 x^2 for x near 0.
For x ? 0.
(1 - cos x) / x^2 ?
1 - cos x ?
cos x ? 1 -

(c) Use your answer to part (b) to approximate cos(0.06).

(d) Use a calculator to approximate cos(0.06) to four decimal places.

Compare the result with part (c).
The result from part (c) is the same to four decimal places.
The result from part (c) is not the same to four decimal places.

Added by Matthew B.

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