8. Find the exponential Fouvier series for the function f..(t)... f(t) = 2t 1.f.t.<..... *** ·2=jn π (2 - jn) jnitt e ·ans: f. (t) = 1 sinh2... - e ·e... 2-jnt +1( n=-x "no"

Q: 00 f(x) = Σχ* k=0 = 1 1 and S(x) = Ext. k=0 The remainder in truncating the power series after n…

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Q: (b) Find the Taylor's series generated by the following function at x = a = 2 f(x) =x' – 2.x+ 4.

A: Given that, fx=x3-2x+4 Given point is x=a=2

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

A: Given power series for the function fx is fx=∑n=0∞3n+1n!x+23n

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: Find the Maclaurian series for the function f(x) = e Select one: O a. O b. O C. O d. e = + 110 = e…

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Q: Q. 29. Calculate harmonic from the following continuous series: Class Interval : 0-10 10-20 20-30…

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Q: 6. Find the Maclaurin series for g(x) S™ g(t) dt. = cos x - 1 + −1+1/2/22 x² and h(r) =

A: The above series is the Maclaurins series for g(x).

Q: /3 In (x + 1) The series representing the integral - dx is given by OA. (-1)"+1 3" n2 OB. (-1)"+1…

A: To find: Series representation of ∫013lnx+1xdx

Q: Explore the uniform convergence of the functional series >- sin nx on the set 3" +x* E = (-0,+0).

A: The given series is, ∑n=1∞n2 sin nx3n+x2

Q: 1. (i) Give the Fourier sine series expansion of f(t) = cos(t) on the interval 0 < t < a.

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Q: Q.2\ The series E is n(1+ln(n))

A: ∑n=1∞1n1+lnn

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

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Q: Q2 Let f(x) = sin(a²)da. Q2.1 Express Q2.2 I sin Q2.3 sin(x²) dx as an infinite series. Use the…

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Q: Develop sin t in the Half-Range cosine series in the interval 0<t<L. L :(0)\ novo ms 10l

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Q: Let f(x) = for sin(t²) dt. Find f" (x).

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. Does the sine series 1 sin (nA x) n=1 converge in the mean-square sense to a function f e L²(0,…

A: Given series is  ∑n=1∞1nsin nπx. To check the convergence of this series in the mean square sense.…

Q: Observe the function X f(x) = (1+2x)² In order to find the power series for this function, complete…

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Q: /31 (3 In (x+ 1) The series representing the integral -dx is given by O A. Σ (-1)"+1 n=1 3" n2 Σ n=1…

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Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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

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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…

A: The function is defined by fx=0if 0&lt;x&lt;π21if π2&lt;x&lt;π We have to evaluate the half range…

Q: Consider the function f(x) = tan ¯¹ (x³). a. Differentiate the Taylor series about 0 for f(x). b.…

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Q: 4. The Riemann zeta function is defined as ((x) = = n² (a) For which real numbers x is ((x) defined?…

A: Given that the Riemann zeta function is defined by, ζx = ∑n=1∞ 1nx. (a) The objective is to find the…

Q: a) With explanation, use the already-known Maclaurin series for e“ to obtain the Maclau- rin series…

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Q: Use your knowledge of the Maclaurin series for f(x) = e" to find the Maclaurin series for g(x) =…

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Q: Use the Maclaurin series for function f(x) = tan-¹ x to find the first four nonzero terms of the…

A: (a). Given that the function is                                 f(x)=tan-1(x).      To find the the…

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: 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: (a) Find the Taylor's series for the function f(x)= sin x at x = (b) Using L'Hospital 'rule to find…

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Q: a. Series for sinh lx Find the first four nonzero terms of the Taylor series for sinh x = dt V1 + f°…

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Q: If f(t)= t2-2t where 0< t< find the following 1) The cosine series. 2) The sine series.

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Q: Determine an odd or even periodic extension of the presented function and determine the Fourier…

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

A: Fourier series

Q: Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b)…

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