(b) Expand f(x) = x as a sine series in the half interval (0, L). Sketch the series you have found (right-hand side of Ans.) over (-2L, 2L). AL ANS. X = sin πT 2n+1 (2n+1)лx L n=0

Q: Find the half-range sine and cosine series 。cx<手 for the function fou=

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Q: 1 where -1. n=0 n sum of ) 3" n=1 (Hint: This looks like a power series that has been evaluated at a…

A: Series summation

Q: +x (-1)" Given cos(x) = (-1)". n=0 (2n)! -x2n for all x E R, %3D 1. Express the integral cos x dx as…

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Q: 4. Find (a) the Fourier cosine series, (b) the Fourier sine series. Sketch f(x) and its two periodic…

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Q: Differentiate the given series expansion of f term-by-term to obtain the corresponding series…

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Q: (-1)" 2n+1 Use the power series sin x=E; to approximate (by using four terms) the value of (2n+1)!"…

A: Let's replace x by x2 to obtain: Let's now expand up to four terms to get:

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

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Q: (-1)"x2" (2n)! +00 1. For all x ER, cos x = Σ n=0 a. Find a power series that is equal to x cos(x)…

A: Given that, cos x = ∑n = 0∞(-1)nx2n2n! a) Find the power series equal to x cos x2 b) Differentiating…

Q: For all x E R, e* = Ln=0 +0+ n! Express f (x) = x e* as a power series.

A: We have to expressf(x)=x2ex of a power series

Q: (8) a) Using the Maclaurin series for f(x )= cos x find the first four nonzero terms of cos( x' ).…

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Q: 3. If we know that > ak = 10,000, then what can we way about lim ay? %3D k=1

A: Explanation of the answer is as follows

Q: Let the improper integrals " sin(-)dx and sin?()dx (i) Write down the first 3 terms of Maclaurin…

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Q: Find a power series for the function centered at 0. 3+x? O(-1)"x" Σ n=0 3" n=0 3 +1 5(-1)"x" +1 n=0…

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Q: Fin:d the Fot:ier sine seri:s in P T/3, for 0<x<T/3, f(x)= 0, for T/3<x<2r/3, -7/3, for 2n/3<x<r.…

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Q: 4. Obtain (a) the half-range cosine series and f(t)= (b) the half-range sine series for the function…

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Q: f(x) is a function such that the graph of y = f(x) consists of a line segment as shown in the…

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Q: 1. You are given that tan-1 x = x-x3 +x 5 – ÷x' + …· for |x| <1. Use the given series to obtain a…

A: (a)-According to question given thattan-1(x)=x-13x3+15x5-17x7+.... for |x|&lt;1Let f(x)=tan-1xNow…

Q: 4) (a) Find a deqree 3 power series for the function sin(x) centered at T fla) = f (2) + f(a) (x-a)…

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Q: Q5. Let the improper integrals, sin()dx and sin² ()dx (i) (ii) Write down the first 3 terms of…

A: Introduction: Sometimes the Maclaurin series is very efficient to integrate a function. The power…

Q: 2. Determine the Maclaurin Series (5th approximation) of the function defined by f(x) = sin x .

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Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: Find (a) the Fourier cosine series (b) the Fourier sine series. Please list the answer to at least 3…

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Q: Compute the Fourier sine series of S 1, 0<x < 1, ={2, 1sx<2, 2, 1<x < 2, on [0, 2]. Sketch both the…

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Q: 6. Evaluate the indefinite integral as an infinite series. (b) / sin z (a) / r cos(r)dr

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Q: 8. One of the fastest series for (T/4) is: 1 + 2 tan 8 1 =6 tan- 4 + tan 57 239 Use the series below…

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