Q4) A. Find the Fourier series of the periodic function -K when -n < x < 0} K when f(x) = *, and f(x) = f(x+ 2n) 0

Q: 6. Assume that the Fourier series of a function (x) on [-L, L] converges to f(x). (a) Derive the…

A: Given- Assume that the Fourier series of a function fx on -L, L converges to fx.  To find-  Derive…

Q: 4. Sketch several periods of the following function: f (x) 0,- pi<x<0;1,0<x<pi/2;0,pi/2<x<pi Expand…

A: Given the function is fx=0-π&lt;x&lt;010&lt;x&lt;π20π2&lt;x&lt;π

Q: 3. (x) =|sin.x| if -p £x£p. Find the Fourier series of f(x) and the result of (2k)-1

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Q: If f(x) = |sinx| in (-1,1) is expressed as Fourier series, then the coefficient of sin5x is 5 ?لكر…

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Q: Define the sequence of functions {fn(x)} on [0, 1] by { 2n2x; 2n(1 — пх); 0; fn(x) = 2n 1 n (a)…

A: Given: fn(x)=2n2x;            x≤12n2n(1-nx);    12n&lt;x ≤1n0;              1n&lt;x, x∈[0, 1].

Q: For x² +nr+1, n = N (the set of natural numbers), 2sin(x²-1)-sin 2(x²-1), sin(x²-1)+sin 2(x²-1)" the…

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Q: Example 6. Find the Fourier series for the function f (x) = 1, -1, if -n < x <- if - <*< if < x < T…

A: The following is the given function:   fx=-1,if -π≤x≤-π20,if -π2&lt;x≤π21,if     π2&lt;x≤π It is…

Q: Find the coefficient b, of the Fourier series representation of the function with period T= 1/50…

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Q: A periodic function is defined in one period as |-sin(폭),-2sx<-1; f(x)={ 1 [x+1, -18x50.

A: In this question, we draw the function in a given domain and find the Fourier series of the…

Q: Q3. (a) Write down the function corresponding to the graph given below. Is the function even or odd…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. If the…

Q: 3) Let f (x) be defined as -1 < x < 0 f(x) = (0, lx + 1, 0<x<1 a) Find the Fourier series of f,…

A: A Fourier series is the series expansion of a periodic function in terms of sine and cosine…

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Q: Q (4)- Find Fourier series for the function: - 2 <t <0 2 f(t) = (4 for for 0 <t< 2

A: Given that, f(t)=-2-2&lt;t&lt;040&lt;t&lt;2 The aim is to find the fourier series. The formula for…

Q: (b) You are given that the Fourier series for f on the interval (-7, 7) is [a, cos(nx) + b,…

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Q: 4х Obtain the Fourier series for the function f(x)=1 1+ 3 <x< 0 2 1A. and 4.x ) <x < 3 f (x+3) =…

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Q: f(x) = cosh(x); -T <x< T etch the function. Determine whether it is even or odd. Expand it in an…

A: Expand the given function in an appropriate Fourier series.

Q: (b) Consider the function f defined by f(x) = +x, if-*< x < 0, if 0<x<T. R-X. and f(x+2nx) = f(x).…

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Q: Let f(x) be a periodic function of period 27 defined by f(r) = x - x2 in (-7, 7). (i) Draw the graph…

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Q: 0, 4. Consider the function f defined on (–x, ), ƒ(x) = —л an cos(nx) + b, sin(nx). 2 n=1 (a)…

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Q: Q.1/Find the fourier series for the following function: St-n ,0<t<n ,T<t< 2n f(t) %3D

A: The Fourier series of given function is given as follows

Q: Q5): By using Fourier series solve the period below: -2, -2 <t<0 f (t) = 2, () <t < 2 If the…

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Q: 5. Is the given function even or odd or neither even nor odd? Find its Fourier series be if p = 1.…

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Q: find Fourier coefficients

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Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: Exercise 4. Consider the following function f(x) = 2|x| if -л≤ x ≤π, extended to the entire real…

A: Part (a)Given the function f(x) = 2|x| for −π≤x≤π, which is extended as a periodic function with a…

Q: 37. f(x) = x + 1, 0 <x< 2

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Q: ) Find Fourier series of the periodic (T = 2T) function f(x) = x² ,- n < x < n

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Q: find the nth Maclaurin polynomial for the function

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Q: Q7. Find the Fourier series of the signal f(t), with period 27, given on the interval [-, π] by…

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Q: Q4: A. Find The Fourier series for the function defined by 2k - (x) if 0 < x <: f(x) = 2kx (1 – x)…

A: Given f(x) =      2kl(x)       if 0≤xl22kxl(l-x)     if l2≤x≤lwe have to find the fourier series for…