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)

Solutions

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

Next > < Previous

Related Solutions

Find the absolute max and min of f(x)= e^-x sin(x) on the interval [0, 2pi] Find...

Find the absolute max and min of f(x)= e^-x sin(x) on the interval [0, 2pi] Find the absolute max and min of f(x)= (x^2) / (x^3 +1) when x is greater or equal to 0

Find the four initial terms of the Maclaurin series for f(x) = tan x

Find the Maclaurin series of the function f(x)=(3x2)e^−4x (f(x)=∑n=0∞cnxn)

1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then determine interval of...

1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then determine interval of convergence. 2. Find the coeffiecient on x^4 in the Maclaurin Series representation of the function g(x) = 1/ (1-2x)^2

1) Find the Taylor series (to second order terms) of the function f(x,y) = x^2 −4x...

1) Find the Taylor series (to second order terms) of the function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y = −1. 2)Explain why the corresponding Taylor Series (to third order terms) will be the same as the second-order series.

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a so that f(x) is a probability density function b)What is P(X<=1)

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing....

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing. List the x coordinates of all local minima of f. If there are no local maxima, enter 'NONE'. List the x coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'. Find the second derivative of f: Use interval notation to indicate the interval(s) of upward concavity of f(x). Use interval notation to indicate the interval(s) of downward concavity...

Find the first five nonzero terms of the Maclaurin expansion of f(x)=e^-xcos(x) (Use symbolic notation and...

Find the first five nonzero terms of the Maclaurin expansion of f(x)=e^-xcos(x) (Use symbolic notation and fractions where needed.)

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x;...

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x; f (0) = 2 2) A rectangular box is to have a square base and a volume of 20f t^3 . If the material for the base costs 30¢/f t^2 , the material for the sides costs 10¢/ft^2 , and the material for the top costs 20¢/f t^2 , determine the dimensions of the box that can be constructed at minimum cost.

Find the Taylor series for f ( x ) centered at the given value of a...

Find the Taylor series for f ( x ) centered at the given value of a . (Assume that f has a power series expansion. Do not show that R n ( x ) → 0 . f ( x ) = 2 /x , a = − 4

Subjects