Q NO 1: (a) Expand the given function in a Fourier series f(x) = 2-x, 0

Q: -(x)) %3D 6. (X)f 1-T, て 21 3L Sheet No,2 (c) Fourier series %3D 2. Expand the given function in an…

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Q: . consider the function: [1+x, | 2.x – 1, 0<x <1 -1<1<0 f(1) = (i) Find the Fourier Series of f and…

A: We are given a piece-wise defined function, and we have to find its Fourier series expansion.

Q: 5. Find the Fourier Series of the function: [0. S0, -7<x<0 0 <x< T f(x) (1,

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Q: M=2 2. Find the value of an (n + 0) in the Fourier series expansion of the functions f (x) = sin(Mx)…

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Q: Tt, B. Find the Fourier series for the f (x), if f(x) = {," - T < x < 0 0 < x < n %3D

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Q: 2. Find the value of an(n + 0) in the Fourier series expansion of the functions f(x) = sin(Mx)…

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Q: (x, b. Find the Fourier sine series for this function: f(x) = 0 < x < T/2 0, <x< n and sketch odd…

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Q: 3 Determine the Fourier series for the function defined by f(x) = 2x 0<x< 2n f(x+ 2m) = f (x)

A: Hint: Fourier series for the function in the interval 0&lt;x&lt;2π fx=a02+∑n=0∞ancosnx+∑n=0∞bnsinnx…

Q: 1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T<x< πT.

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Q: Find the Fourier series expansion of the periodic function whose definition in one period is; -T<I…

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Q: Find the Fourier series expansion of the periodic function whose definition in one period is: TL…

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Q: Q2 (a) Explain the difference between even and odd Fourier series function. (b) Find the Fourier…

A: Fourier series

Q: -2 (-T<Iく0) (0 <t<x) f(t) b.

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Q: Q1: Find with sketch the Fourier coefficients and Fourier series of the function f(x) defined by…

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Q: Q1: 1. Find The Fourier series for the function defined by (x - f(x) = {* – 2 0 < x< 4 1 -4 <x< 0S…

A: As per guideline, one question at a time

Q: 8. Expand the given function in a Fourier series: f(x)= x +1, 0 < x <1

A:

Q: Write Fourier series for the function y=4n-k T≥X≥0

A: A Fourier series is a sum that represents a periodic function as a sum of sine and cosine waves.…

Q: (a) Assume that f(x) is function defined by -4 if -T≤ x < 0, f(x) = for 0≤x≤T. (i) Expand the…

A: According to guidelines we can solve only one problem

Q: Q NO 1: (a) Expand the given function in a Fourier series f(x) = 2 - x, 0<x<2

A: Given

Q: (a). Determine the Fourier series for the 2p-periodic function given on the interval [0,2p) by f(x)=…

A: a. Hint: The Fourier transform of a function f(x) is…

Q: Find the Fourier series of the odd-periodic extension of the function f(x) = 2x for x € (0,2).

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Q: 3 1. Find the Fourier series on -≤x≤ for f(x) = sin ³ x, which is an odd function.

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Q: ii) Consider the following differential equation on (-1,1) (1-x²)y" - 2xy + n(n+1)y=0 a) Write this…

A: Given: The differential equation, 1-x2y''-2xy'+nn+1y=0 on -1,1. (a.) To Write: This equation in…

Q: If f(x) = x³ + x is a periodic function with period 2π, then the Fourier series will have the…

A: Solutions

Q: 5. Find the Fourier sine series expansion of the funct.f(x) = x² + 5, 0 < x < n.

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Q: 2x 1- if 0<x<a/2 Find the Fourier series of f(x)= f(x+7)= f(x). if a/2<x < T

A: The given problem is to find the Fourier series expansion of the given periodic function with period…

Q: 2. (a) Find Fourier Series representation of the function with period 2 defined by f(t)=sin (1/2).

A: Sol:- Fourier series of function fx on interval -L≤ x≤ L is defined as: x=A0+∑n=1∞ An·cosnπxL+∑n=1∞…

Q: Q4) A. Find the Fourier series of the periodic function -K when -n < x < 0} K when f(x) = *, and…

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Q: 1. Find The Fourier series for the function defined by 0 <x< 4 1 -4 <x< 0J f(x) = {* – 2

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Q: -k, -2 < x <0] f) = <xく2」 0 < x < 2 ]

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Q: ーt ーTくt<0, f(t) = +t 0 <t< n.

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Q: Q1: Find The Fourier series for the function defined by (X – 2 f(x) = {*´ 0 0 < x<4 -4 < x< 0S %3D

A: We have to get Fourier series

Q: 8. Find the exponential Fourier Series for the function f(t) = 2t .............. - 2 = jnm (2 fm)…

A: Given that, ft=e2t   -1&lt;t&lt;1 Find the exponential Fourier series for the given function. As we…

Q: 6. Write the Fourier Sine series for f(x) =R - x (0<x<7). sin nx Ans. 2

A: To find the fourier sine series of the given function f(x) = π-x in half range 0 to π we use the…

Q: Q1: Find the Fourier coefficients and Fourier series of the triangle function f(x) defined by +x, if…

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Q: 1. Fl the fourier series representing, f(x)=x, 0<x< 2 and sketch its graph from x =-4 to x=4n.

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Q: Q1/ Expand f(x) = x, 0<x<L, (a) in a cosine series, (b) in a sine series, (c) in a Fourier series. y…

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Q: 1. Find the Fourier Series of the function: (0, ´0, -T < x < 0 f(x) 0 <x< T

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Q: f(x)= re¯² (-1<x< 0).

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Q: 2. Sketch the graph of f(x)=-x, 0<x<*, f(x)=f(x + 2). Then, find the Fourier sine series of f(x).

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Q: Q#10: Develop f (x) in the Fourier series, if defined as: (i) : f (x)= 3x cos 2x, – a <x <n. (-2x,…

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Q: 4. Find the Fourier series for the Function f(x) = |x| ,When -n< X<n.

A: The given function is: f(x)=|x| ;          -π≤x≤π Therefore: f(x)=-x            if  -π≤x&lt;0   xif…

Q: {: (z) -T <I<0

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Q: Determine Fourier Series representation of the function with period 2 defined by f(t)=t², 0<t< 2.

A: Given that, f(t) = t2 and the interval is   0 &lt; t &lt; 2 we have to calculate the fourier series…

Q: 1. Find The Fourier series for the function defined by 0 <x < 41 -4 < x < 0J f(x) = {* – 2

A: The objective is to find the Fourier series of the function defined by fx=x-20&lt;x≤40-4≤x≤0

Q: 4 What is the value at x = 4 of the Fourier series for the function defined by 2 0<x< 2 2<x < 4 4 <…

A: We have to find the Fourier series for the given function at x=4

Q: Q1// Find the Fourier series of the periodic function f(x) = cos (x +), 2

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Q: Expand the given function into a Fourier series: f (x) = x, 0 <x <π

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.