Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants a1, a2, ..., An· Show that for each k = 1, 2, ..., n, T = f(x) sin(kæ) dæ. ak
Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants a1, a2, ..., An· Show that for each k = 1, 2, ..., n, T = f(x) sin(kæ) dæ. ak
Chapter3: Functions
Section3.5: Transformation Of Functions
Problem 5SE: How can you determine whether a function is odd or even from the formula of the function?
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Question
Let n and m be integers.
![Suppose we define a function f(x) by
f(x)
= a1 sin(x) + a2 sin(2x) +·
..+ an sin(nx),
for constants a1, a2, ·
An.
•.• ,
Show that for each k = 1,2,..., n,
1
ak
f(x) dx.
sin(kx)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2532cff-0943-446b-9098-9d1ce43f612f%2F0a00d34f-e7e3-4033-85d0-f5b513c3b5fb%2Fl8vwrb5_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose we define a function f(x) by
f(x)
= a1 sin(x) + a2 sin(2x) +·
..+ an sin(nx),
for constants a1, a2, ·
An.
•.• ,
Show that for each k = 1,2,..., n,
1
ak
f(x) dx.
sin(kx)
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