Find the half range sine series for f(x) = x( - x) in (0, 1).

Q: Obtain the half-range sine series for the function f(x) = x² in the interval 0<x<3.

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Q: Obtain the half range sine series for ex in (0,pie)

A: We have to obtain half range for                                                        f(x)=ex  in…

Q: Obtain the half-range sine series for ex in (0,π)

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Q: Q4. Find the Fourier sine series for the function: f(x)= 0 for 0<x< 1/1 for 1/1/1<x<

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Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: 3. Determine the half-range sine series for the function defined by: x. 0<x< f) =

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Q: f(x) = x + 1 0<xくT

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Q: Expand f(x) =5xas a half-range Fourier sine series in the range 0 < x<T, and sketch the function…

A: See the attachment

Q: Determine the half range Fourier Sine Series for the function f(t) = sin t Ost2

A: See the attachment

Q: 1. Find the Fourier Sine Series for f(x) = sinx (0 < x < n ) %3D

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Q: Write the sigma form for sin(x^2), Write the first 4 terms of the series approximation, and use the…

A: The given information is sinx2. Write the first 4 terms of the series approximation. Here we use…

Q: 2- Determine the half-range sine series for the function defined by: x, 0 <x < 2 f(x)= 0, <x < T

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Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<T Sketch…

A: If the function is over half 0 to L then it is half range Fourier  series the half range Fourier…

Q: Find the Fourier Sine series of the function f(x) = cos(x) for x e [0, T]

A: Given : f(x) = cos (x)  for x€[0,π]

Q: 31. f(x) = 1, 0≤x≤; cosine series, period 27

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Q: ". Expand the function f(x)=|x, - T < x < A in an appropriate cosine or sine series.

A: Given that, fx=x ,  -π&lt;x&lt;π  Here, -L , L=-π,π Hence, L=π As the given function is even…

Q: The Maclaurin series of sin.x is given by r x7 + 5! 7! sinx 1! 3! Use the above expansion to check…

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Q: Determine the half-range sine series for the function defined by: x, 0<x < f(x) = 0, %3D <x < T 2-

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Q: Find the half-range sine series of f(x) = ex on [0, 1]

A: The half-range sine series of a function f(x) on an interval 0,a is given by, fx=∑n=1∞ bn sinnπxa…

Q: 2. Find the sine series of Sx, 0 <x < T/2 T/2<x< T f(x) = TT - X, - x,

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Q: Compute the Fourier cosine series of f(x) = 1+ x, 0 < x < a if ƒ(x +2x) = f(x). Sketch both the…

A: To calculate the Fourier cosine series of below function. fx=1+x,0&lt;x&lt;π

Q: Use series to estimate the integral 1-cos x dx x2

A: Series

Q: Find (a) Fourier Sine Series, and (b) Fourier Cosine series for the function f(x) = |x| , 0 < x < L

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Q: Find Fourier series for the function f (x) = x\,- <x< T

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Q: 6. Find the sine series of 0 < x < T/2 T/2 <x < T х, f(x) TT - x,

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Q: Find the Maclaurin series for f(x). f(x) = sin- 3

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Q: The Maclaurin series of sin.x is given by * x7 +. 7! sinx = - 1! 3! 5! Use the above expansion to…

A: Given: Differential equation xy''+sinxy=0. Maclaurin series of sinx,…

Q: Find the power series representation for the derivative of the function

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Q: 2. Find a power series representation for the function. sin x f(x) =

A: given : f(x)=sinx/x we have to find its power series .this can be done using maclaurin series…

Q: (III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).

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Q: Which of the following is a power series about base point 0 for the derivative of f(x) = z²e-²?

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Q: Find the power series for f(x) = ln(1 − x) centered at x = 0 by using term-by-term integration or…

A: Given  fx=ln1-x

Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<n Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the Fourier sine series of the function f(x) = x² cos x on the interval [-L, L].

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Q: Find Half range sine series of the function: -3 < x < 0 0 < x < 3 1.

A: Solution:

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: find the integral of sin(x^2) by using the mclauren series of sin(x)

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Q: 2 Obtain (a) the half-range cosine series and (b) the half-range sine series for the function 0. 0(…

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Q: Find the half-range sine series for the function f(t)=nt-t², in the interval 0<t<n.

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Q: Use term-by-term differentiation or integration to find a power series centered at a = 0 for: – 6z5…

A: Given, fx=-6x51+x62 Find the power series representation of the function f (x).

Q: obtain the half range sine series for ex in (0,pie)

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Q: Write the first 4 nonzero terms of the integral I= x sin(x)dx using the Maclaurin series for sin(y).

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Q: Express f(x) = – x, as a Half Range Fourier sine series over the interval 0 <x < 1.

A: Given, fx=-x Find Half range Fourier sine series over the interval 0&lt;x&lt;1.

Q: 2. Find the sine series of Sx, 0 <x < T/2 f(x) п - х, T/2 < x < T

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Q: Q3 Find the half-range Fourier cosine series of f(x) = (1 - x)" in the interval (0, n).

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Q: The Maclaurin series of sinx is given by sinx = 1! +.... 7! - 3! 5! Use the above expansion to check…

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