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Elementary Calculus Infinite Series Taylor's Formula Examples Example 3: MacLaurin's Formula for f(x) = sin x
 

Example 3: MacLaurin's Formula for f(x) = sin x

Find MacLaurin's Formula for f(x) = sin x. The derivatives are

f(x) = sin x

f(0) = 0

f'(x) = cos x

f'(0) = 1

f"(x) = - sin x

f"(0) = 0

f(3)(x) = -cos x

f(3)(0) = -1

f(4)(x) = sin x

f(4)(0) = 0

f(5)(x) = cos x

f(5)(0) = 1

MacLaurin's Formula for 2n terms is

09_infinite_series-701.gif

09_infinite_series-702.gif

For all t, |cos t| ≤ 1, so we have the error estimate

09_infinite_series-703.gif

Last Update: 2006-Nov-15