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Social Science-5Using a Taylor series, find the polynomial of least degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10XF(x)sin t dt[0,1]F(x)
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Using a Taylor series, find the polynomial of least degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10
X
F(x)sin t dt
[0,1]
F(x)](https://prod-qna-question-images.s3.amazonaws.com/qna-images/question/32a17b0d-da1e-491a-8c96-0f01cecd5dd0/bafb2474-05f7-41f7-b5ea-d3b73d5306f0/spp9jz5d.png)
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-5 Using a Taylor series, find the polynomial of least degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10 X F(x)sin t dt [0,1] F(x)
Expert Answer
The general Taylor series for sin x at x = 0 is as follows.
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sinx x 3! 5! Then sin 2_ t° t!° /4 3! 5! 7! t61014 dt 3 (7)3! (11)5! (15)7! 3! 5! 7!
Here the interval for x is [0,1].
Since the lower limit of the integration is 0, the d...
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1 =0.3333333-.. 3 3 0.0238095. (7)3! (7)3! = 0.000757575--. (11)5! (11)5! 15 -0.1323x10 (15)7! (15)7! 119 1.4503x 107 is greater than 105 19 (19)9! (19)9!
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