If f(x) = x for 0 < x < n/2 and f(x) = a – x for 1/2 < x < n, show that the cosine series for this function is cos 2(2n – 1)x (2n – 1)² 2 f(x)= -- 4 T 1.

Q: Consider the function given by the following power series. Зп + 1 f(x) = Σ (x+ 2)3n п! n=0 Find the…

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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

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Q: 18. Find the Fourier sine series in 7/3, for 0<x<T|3, f(x)={ 0, for /3<x<2n/3, (-7/3, for 2r/3<x<n.…

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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: cosh(x) dx is The power series representation of

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Q: find the first few terms of the taylor series of f(x) = 1/x at a = 1, solve by replacing x with…

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Q: Consider f(x) = 1 – x for 0 1: an b) O an = c) O ao = 1/2, and for n > 1: a, = 4(1+…

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Q: (d) f(x) = cos(x) (e) f(x) = x² sin(x)

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Q: 1. Expand f(x) = π 0 if 0 < x < 2² ㅠ if <x< ₁ π, 1 if in a half-range: (a) Sine series. (b) Cosine…

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Q: (-1)" (13z)" is 00 The first derivative of the power series f(x) = n! O -13 f(x) O f(x) O - f(r) O…

A: We need to evaluate the first derivative of the following power series : fx = ∑n=0∞-1nn!13xn

Q: (a) |r cos(a*)dz

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: (a) Find the Taylor's series for the function f(x)= In(3+4x) at x= 2.

A: The Tayler's formula can be used to calculate the expansion of the function. The formula for the…

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Q: 2 The power series representation of the function f(x) = is X- 1

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Q: half range sine series

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Q: 5x Represent the function as a power series f(x) = >, Cnx" 6+ x n=0 Co = C1 = C2 = C3 = C4 =

A: According to the given information, it is required to represent the function as power series.

Q: f(x) = | tan-1(x9) dx f(x) = C + > n = 0

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Q: 5. Find the sine series of 0 < x < T/2 Sx, f(x) T – x, T/2 <x<

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Q: Let f(x) = cos (3x²) - 1 x² = Evaluate the 10th derivative of f at x = 0. f(10) (0) = Free-form Snip…

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Q: 3. Generating Functions (a) Find the coefficient of a" in the series y + 5a².

A: A generating function is very significant in discrete mathematics. A function or a sequence can be…