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Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct?
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Periodic function can be expressed in a Fourier series of the form, f(...
Introduction:
A periodic function is a function that repeats its values at regular intervals. Fourier series is a mathematical tool used to represent periodic functions as a sum of sinusoidal functions. It expresses a periodic function as an infinite sum of sine and cosine functions with different frequencies.
Given:
We are given two periodic functions, f(x) = cos²x and f(x) = sin'x, and we need to find the coefficients for their respective Fourier series.
Fourier Series:
The Fourier series representation of a periodic function f(x) is given by:
f(x) = (a₀/2) + Σ(aₙcos(nx) + bₙsin(nx))
where a₀, aₙ, and bₙ are the coefficients of the Fourier series.
Finding the Coefficients for f(x) = cos²x:
To find the coefficients for f(x) = cos²x, we need to calculate the values of a₀, aₙ, and bₙ.
Step 1: Calculate a₀:
The coefficient a₀ is given by:
a₀ = (1/π) ∫[0, 2π] f(x) dx
For f(x) = cos²x, we have:
a₀ = (1/π) ∫[0, 2π] cos²x dx
Step 2: Calculate aₙ and bₙ:
The coefficients aₙ and bₙ are given by:
aₙ = (1/π) ∫[0, 2π] f(x) cos(nx) dx
bₙ = (1/π) ∫[0, 2π] f(x) sin(nx) dx
For f(x) = cos²x, we have:
aₙ = (1/π) ∫[0, 2π] cos²x cos(nx) dx
bₙ = (1/π) ∫[0, 2π] cos²x sin(nx) dx
Finding the Coefficients for f(x) = sin'x:
To find the coefficients for f(x) = sin'x, we need to calculate the values of a₀, aₙ, and bₙ.
Step 1: Calculate a₀:
The coefficient a₀ is given by:
a₀ = (1/π) ∫[0, 2π] f(x) dx
For f(x) = sin'x, we have:
a₀ = (1/π) ∫[0, 2π] sin'x dx
Step 2: Calculate aₙ and bₙ:
The coefficients aₙ and bₙ are given by:
aₙ = (1/π) ∫[0, 2π] f(x) cos(nx) dx
bₙ = (1/π) ∫[0, 2π] f(x) sin(nx) dx
For f(x) = sin'x, we have:
aₙ = (1/π) ∫[0, 2π] sin'x cos(nx) dx
bₙ = (1/π) ∫[0,
A periodic function is a function that repeats its values at regular intervals. Fourier series is a mathematical tool used to represent periodic functions as a sum of sinusoidal functions. It expresses a periodic function as an infinite sum of sine and cosine functions with different frequencies.
Given:
We are given two periodic functions, f(x) = cos²x and f(x) = sin'x, and we need to find the coefficients for their respective Fourier series.
Fourier Series:
The Fourier series representation of a periodic function f(x) is given by:
f(x) = (a₀/2) + Σ(aₙcos(nx) + bₙsin(nx))
where a₀, aₙ, and bₙ are the coefficients of the Fourier series.
Finding the Coefficients for f(x) = cos²x:
To find the coefficients for f(x) = cos²x, we need to calculate the values of a₀, aₙ, and bₙ.
Step 1: Calculate a₀:
The coefficient a₀ is given by:
a₀ = (1/π) ∫[0, 2π] f(x) dx
For f(x) = cos²x, we have:
a₀ = (1/π) ∫[0, 2π] cos²x dx
Step 2: Calculate aₙ and bₙ:
The coefficients aₙ and bₙ are given by:
aₙ = (1/π) ∫[0, 2π] f(x) cos(nx) dx
bₙ = (1/π) ∫[0, 2π] f(x) sin(nx) dx
For f(x) = cos²x, we have:
aₙ = (1/π) ∫[0, 2π] cos²x cos(nx) dx
bₙ = (1/π) ∫[0, 2π] cos²x sin(nx) dx
Finding the Coefficients for f(x) = sin'x:
To find the coefficients for f(x) = sin'x, we need to calculate the values of a₀, aₙ, and bₙ.
Step 1: Calculate a₀:
The coefficient a₀ is given by:
a₀ = (1/π) ∫[0, 2π] f(x) dx
For f(x) = sin'x, we have:
a₀ = (1/π) ∫[0, 2π] sin'x dx
Step 2: Calculate aₙ and bₙ:
The coefficients aₙ and bₙ are given by:
aₙ = (1/π) ∫[0, 2π] f(x) cos(nx) dx
bₙ = (1/π) ∫[0, 2π] f(x) sin(nx) dx
For f(x) = sin'x, we have:
aₙ = (1/π) ∫[0, 2π] sin'x cos(nx) dx
bₙ = (1/π) ∫[0,
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Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct?
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Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct?.
Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct?.
Solutions for Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? in English & in Hindi are available as part of our courses for Physics.
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Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct?, a detailed solution for Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? has been provided alongside types of Periodic function can be expressed in a Fourier series of the form, f(x) = (a, cos(nx) b sin(x)) The functions f(x) = cos²x and f(x) = sin'x are expanded in their respective Fourier series. If the coefficients for the first series are a and b and the coefficients for the second series are a and b respectively, then which of the following is correct? theory, EduRev gives you an
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