set up the mclaurin series for f(x) = e^x....afterwards find the terms needed to approx. f(2pi)...

set up the mclaurin series for f(x) = e^x....afterwards find the terms needed to approx. f(2pi) for an error less than 10^-7... I'm not sure what to do with that f(2pi)

Expert Solution

To find the value of 'n', there is no other way than to run a simulation or do hit & trial to check the value of 'n' which satisfies this inequality.

Using excel, you get following output for different values of 'n' -

n	Rn(x)
1	10570.18
2	22138.14
3	34774.5
4	43698.93
5	45761.41
6	41075.35
7	32260.5
8	22522.08
9	14151.04
10	8083.055
11	4232.278
12	2045.553
13	918.0419
14	384.5485
15	151.0118
16	55.81385
17	19.48271
18	6.442814
19	2.02407
20	0.6056
21	0.172959
22	0.047249
23	0.01237
24	0.003109
25	0.000751
26	0.000175
27	3.92E-05
28	8.5E-06
29	1.78E-06
30	3.61E-07
31	7.08E-08

So, we need n = 31 to get the value of f(2) accurate to 10^-7.

So, number of terms needed = n +1

=32

Because the first term is 1.

_________________________

milcah answered 2 years ago

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