Question
Asked Aug 14, 2019
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Help me please

-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)
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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)

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Expert Answer

Step 1

The general Taylor series for sin x at x = 0 is as follows.

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!
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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!

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Step 2

Here the interval for x is [0,1].

Since the lower limit of the integration is 0, the d...

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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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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