Let f be the 4-periodic funtion on R with one period given by if 2x < −1 - 0 f(x) = 1 if - 0 1<<1. if 1 < x < 2 Find the Fourier series of f. Sf(x) = ao + Σαπ ппх ппх an COS + bn sin === 2 2 n=1 1/2 ппх COS +0 2 + ∞ (2sin(npi/2))/(pin) n=1 ппх sin 2 Note: Your coefficients should match the given cos (2) and sin (TI) terms in the above equation. Therefore, do not collapse your coefficients. In particular, do not remove the zero terms and reindex. For what value(s) of x is f(x) equal to its Fourier series Sf(x) on the interval [-2,2]? Give your answer as an interval or union of intervals. x€ (-1,1) For values of a where f(x) Sf(x), evaluate Sf(x). Sf(x) = x
Let f be the 4-periodic funtion on R with one period given by if 2x < −1 - 0 f(x) = 1 if - 0 1<<1. if 1 < x < 2 Find the Fourier series of f. Sf(x) = ao + Σαπ ппх ппх an COS + bn sin === 2 2 n=1 1/2 ппх COS +0 2 + ∞ (2sin(npi/2))/(pin) n=1 ппх sin 2 Note: Your coefficients should match the given cos (2) and sin (TI) terms in the above equation. Therefore, do not collapse your coefficients. In particular, do not remove the zero terms and reindex. For what value(s) of x is f(x) equal to its Fourier series Sf(x) on the interval [-2,2]? Give your answer as an interval or union of intervals. x€ (-1,1) For values of a where f(x) Sf(x), evaluate Sf(x). Sf(x) = x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let f be the 4-periodic funtion on R with one period given by
if 2x < −1
-
0
f(x) =
1
if
-
0
1<<1.
if 1 < x < 2
Find the Fourier series of f.
Sf(x) = ao +
Σαπ
ппх
ппх
an COS
+ bn sin
===
2
2
n=1
1/2
ппх
COS
+0
2
+
∞
(2sin(npi/2))/(pin)
n=1
ппх
sin
2
Note: Your coefficients should match the given cos (2) and sin (TI) terms in the
above equation. Therefore, do not collapse your coefficients. In particular, do not
remove the zero terms and reindex.
For what value(s) of x is f(x) equal to its Fourier series Sf(x) on the interval
[-2,2]? Give your answer as an interval or union of intervals.
x€ (-1,1)
For values of a where f(x) Sf(x), evaluate Sf(x).
Sf(x) =
x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc87404db-82a2-44ca-b323-e29be1d430e6%2F30866ef8-9fe6-4750-aef6-9644e9e78787%2Fxdg9wrgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f be the 4-periodic funtion on R with one period given by
if 2x < −1
-
0
f(x) =
1
if
-
0
1<<1.
if 1 < x < 2
Find the Fourier series of f.
Sf(x) = ao +
Σαπ
ппх
ппх
an COS
+ bn sin
===
2
2
n=1
1/2
ппх
COS
+0
2
+
∞
(2sin(npi/2))/(pin)
n=1
ппх
sin
2
Note: Your coefficients should match the given cos (2) and sin (TI) terms in the
above equation. Therefore, do not collapse your coefficients. In particular, do not
remove the zero terms and reindex.
For what value(s) of x is f(x) equal to its Fourier series Sf(x) on the interval
[-2,2]? Give your answer as an interval or union of intervals.
x€ (-1,1)
For values of a where f(x) Sf(x), evaluate Sf(x).
Sf(x) =
x
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