What is the value of (do) for Fourier Series of the function f(x) = x², - TS x < n? %3D 2n3 c) 3 d) * 2n2 2n2 b) 0 f) 3 n? g) None of them a

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: find the fourier series of f(x) = x^2  in the interval [0,2pi]

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Q: (4) In order to determine the sum the value of a that neods to be substituted in the Fourier series…

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Q: Find the Fourier series of the function f(x) = (-4, 4, - π < x < 0 0<x<π

A: Given function, f(x)=-4,-π&lt;x&lt;04,0&lt;x&lt;π The objective is to find the Fourier series of the…

Q: Expand the Fourier series of sinx; 0<a < T, f(æ) = { 0; - T<a < 0 Hence deduce that 1 T-2 1 1.3 3.5…

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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: Find the Fourier series representation of f(x) = x x € [-n, n] Apply Parseval's formula on the given…

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Q: Find the Fourier series Expansion for the function between (-2 < X < +2) F(t) = VN + Nt²

A: Given F(t)=N+Nt2 The fourier series is, F(t)=a02+∑n=1∞ancosnπx2+bnsinnπx2 Where…

Q: 3. Find the complex Fourier Series for periodic extension of: x(t) = sin(2t) %D for 0 <t< 2T

A: Note: Since you have posted multiple questions, according to the policy we are only allowed to solve…

Q: Determine the an of the Fourier Series of: -3, 3, - 1<t<0 f(t) = { 0 <x < 1

A: Given ft=-3-1&lt;t&lt;030&lt;t&lt;1

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: A signal f(t) is defined as f(t) = [3 cos (2nt) + 5sin(2nt)|². Is this a valid Fourier series…

A: step-1given thatf(t)=3cos2πt+5 sin(2πt)2it can be written asf(t)=9 cos22πt+25…

Q: A. Find the Fourier Series af x)= -x- = X+Y 0 4x<

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Q: Find the Fourier Cosine Series of f(x) = 4x²; 0 < x < 1

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Q: 4. Let f(x) = x² – x, 0<x < 1. Find the Fourier cosine series for the even extension of f. %3D

A: Given problem is :

Q: Find fourier series in mathematica 5 f() = x,0<x< 2m

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Q: Find the Fourier series of f(r) on the given interval. πε (-1,0), r € [0, 1). -3 r€ (-1,0), f(x) = 3

A: Consider the given function:  f(x)=-3      x∈-1,03         x∈[0,1) we know that Fourier series…

Q: Assume that there is a Fourier series converging to the function f defined by х, —2 <х < 0, f(x) =…

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Q: find theral form or fourier Series for f(x) = x+\xl in (- T, JJ) and then abtain Complex form?

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Q: Find the Fourier series expansion of F(x) =x/2 + x² in the interval — π≤ x ≤ π

A: Given

Q: What is the value of a0 in Fourier series of a|, where F(x + 2n) = F(x) cos( )+ sin( x)

A: a0=12π∫-ππxdx=22π∫0πxdx=1πx220π=1ππ22=π2

Q: Compute the Fourier Cosine Series for f(x) = -x, 0 < x < 1. Hence, show that Σ(2n-1)² n=1 || 00/7

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Q: Find fe(), the Fourier series expansion of * € [-L, 0), * € [0, L], where k and L are positive…

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Q: Find the Fourier series representation of the loading -ø < 0 < +¢ -n < 0 < -ø, ¢ < 0 < x Pr

A: Given function is periodic with period 2π, bounded and integrable.

Q: Find the Fourier series of the functions Ekez max(1 – |x – k|, 0) - and Ekez max(1 – |r – k/2|,0).…

A: The complete solutions are given below

Q: 1. Obtain Fourier series for the function f(x) given by 3x 1+ 1 1 1 + 32 5? f(x) = Hence deduce…

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Q: Expand f (x) = 2 – x,0 < x < 2 (a) in a cosine series (b) in a sine series (c) in a Fourier series

A: According to the given information, it is required to expand the function:

Q: (a) Find the Fourier series expansion of f(x) = , in -xSxSn. Hence deduce that 12 12

A: We will find out the required value .

Q: Show that the Fourier series for f (x) = x, –n (-1)n+1 n n-1

A: Fourier series of the function

Q: a) Find a Fourier series to represent f(x)=x- x² from x=-7 to x=T , and deduce that 1 + 12 12 22 '…

A: (a) Given,                f(x)=x-x2      from x=-π to x=π.

Q: 6. (a) Express the function f(x) = x in on [0, T] as a Fourier cosine series S(x). What is S(-1)?

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Q: What is the first term of the given Fourier series f(x) = 2 E,(-1)"-l sin () ? %3D Select one: -2…

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Q: Find the Fourier series of the function f(x) = 2L – on the interval [-L, L].

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Q: Find the complex form of Fourier series for e-x in -1<x <1

A: See the attachment

Q: construct the Fourier series for the function f (x) = (T - x)2 for 0 < x < 2n ?

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Q: 6. Find the Fourier series of the function (-n <x < 0) 0, f (x, y) = %3| sin r, (0 < r < n). Use…

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Q: : Develop f (x) in the Fourier series, if defined as: (i): f (x)= 6xsin 5x, – n < x < n.

A: We will find out the required Fourier series.

Q: What is the value of a0 in Fourier series of Jæ|, where F(z + 2n) = F(z) %3D cos( )+ sin( a)

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Q: Find the Fourier sine series of f(x) on 0, 3|| f(x) = 6 – 2x

A: f(x)=6-2x , interval on [0,3]

Q: Find the sum of 1+++t using Fourier series expansion if f(x) a when [0,T] and 2 T-x when [ T, 2 T].

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Q: Find the Fourier series for the function f (x) shown below. Towards which values ​​does this series…

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Q: In a Fourier series, f(x) = x in the interval (- 7,7) then the calculation of b, value is a)…

A: Option (c) is correct.

Q: Find the Fourier series for f(r) = -1 (-x <r < 0) and = 2 (0 <r< T). %3D

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Q: The Fourier series to represent the function f(x)=2x in the range - T to + is 1 2x = 4 sin c,x - sin…

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Q: (b) Obtain the Fourier series expansion of f(x) = x sin(r) on [-Ħ,]. Use the series to deduce 1 1 1…

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Q: 3. [MO31] Find the Fourier series of, - 2< x< -1 f(x) = }-2 - 1<x< 1 1< x< 2

A: The given problem is to find the Fourier series of given function with given period.

Q: The Fourier series of a functionf(x) defined on [-x, n] is given by 1 -cos 3x + 43 1 1 4 + - cos x +…

A: Given Fourier series on [-π, π] is f(x)=4+14cosx+142cos2x+143cos3x+144cos4x+... We can write in the…

Q: Find the sum of 1+1/1^2 +1/3^2 +1/5^2 +⋯, using Fourier series expansion if f(x) = a when [0,π] and…

A: Given:- The sum 1+112+132+152+............ if f(x)= a when 0,π and 2π-x when π,2π

Q: 3. Find the Fourier series of, - n<x<-1/2 f(x) = }0 - 1/2 <x <n/2 1/2 < x <n 1

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.