3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Question 3 and 5
![Exercises and Problems for Section 10.5
EXERCISES
I Which of the series in Exercises 1-4 are Fourier series?
6. Repeat Exercis
1. 1+ cos x + cos x + cos' x + cos“ x + ….
2. sin x + sin(x +1) + sin(x + 2) + ...
7. What fraction o
is contained in t
ics of its Fourie
3.
cos x
+sin x-
cos(2x) sin(2x) , cos(3x) , sin(3x)
4
8.
1
4.
sin x +
sin(2x)
4
3
sin(3x) + ...
For Exercises 8-10,
given functions, ass
2n. Graph the first
function.
5. Construct the first three Fourier approximations to the
square wave function
(X) = {;
-A < x < 0
0 < x < n.
-1
8. f(x) = x²,
9. h(x) =
Use a calculator or computer to draw the graph of each
approximation.
10. g(x) = x,
PROBLEMS
degree Fourier
terval 0 < x <
11. Find the constant term of the Fourier series of the tri-
angular wave function defined by f(x) = |x| for -1 <
x<1 and f(x + 2) = f(x) for all x.
12. Using your result from Exercise 10, write the Fourier
series of g(x) = x. Assume that your series converges
to g(x) for -a < x < n. Substituting an appropriate
value of x into the series, show that
riod is not 2r, y
tution. Notice th
and cos(nx), bu
cos(2rnx).]
16. Suppose f has
Find the fourth-e
00
1
on 0 <x < 2. [E
2k 1
4
17. Suppose that a s
a quantity A and
odic signal A cos
the signal picks u
k-1
13. (a) For-2n < x< 2n, use a calculator to sketch:
sin 3x
i) y = sin x +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f6f9d78-1cfb-42f7-a722-dde7cbe94a91%2F0b948ef2-5708-4996-ba68-2920037e33a6%2Frzp9sr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercises and Problems for Section 10.5
EXERCISES
I Which of the series in Exercises 1-4 are Fourier series?
6. Repeat Exercis
1. 1+ cos x + cos x + cos' x + cos“ x + ….
2. sin x + sin(x +1) + sin(x + 2) + ...
7. What fraction o
is contained in t
ics of its Fourie
3.
cos x
+sin x-
cos(2x) sin(2x) , cos(3x) , sin(3x)
4
8.
1
4.
sin x +
sin(2x)
4
3
sin(3x) + ...
For Exercises 8-10,
given functions, ass
2n. Graph the first
function.
5. Construct the first three Fourier approximations to the
square wave function
(X) = {;
-A < x < 0
0 < x < n.
-1
8. f(x) = x²,
9. h(x) =
Use a calculator or computer to draw the graph of each
approximation.
10. g(x) = x,
PROBLEMS
degree Fourier
terval 0 < x <
11. Find the constant term of the Fourier series of the tri-
angular wave function defined by f(x) = |x| for -1 <
x<1 and f(x + 2) = f(x) for all x.
12. Using your result from Exercise 10, write the Fourier
series of g(x) = x. Assume that your series converges
to g(x) for -a < x < n. Substituting an appropriate
value of x into the series, show that
riod is not 2r, y
tution. Notice th
and cos(nx), bu
cos(2rnx).]
16. Suppose f has
Find the fourth-e
00
1
on 0 <x < 2. [E
2k 1
4
17. Suppose that a s
a quantity A and
odic signal A cos
the signal picks u
k-1
13. (a) For-2n < x< 2n, use a calculator to sketch:
sin 3x
i) y = sin x +
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