Prove that these two E E cos (Tin) não Inn 2 are تم 22=1 convergent (-1) h 22²41

Q: Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is…

A: FSt=a02+∑n=1∞ancosnπt4+bnsinnπt4a0=1.5an=4-1nnπbn=51-2-1nn2π2

Q: 4. Find the Fourier series representation of the function: -1<1<0 (t) = {-. *-1, 0<1<<1 which is…

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Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y = min(X1,..., Xn) is also exponential…

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Q: (5) Solve for n EN. +2 (a) (3) = }(n+²). 5 n (b) (²) > (^).

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Q: Specify c-1, Co, C₁ and p such that the formula g′(s) ≈ k¯²(c_19(s − k) + cog(s) + C₁g(s + k))…

A: Finite difference is a method of numerical analysis which is used to calculate the derivative of a…

Q: The moment generating function at v = 0 is unity. It is given as M x (v )|... = Mx (0) = 1 lv 0

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Q: Pro ve 8さt(.)る %3D (Srh)(らtM ー7 \et: ヒこe

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Q: Differentiate the Newton's Forward formula P, = to + (",")At, +(";")A²to + (",')4³to + (",")4*to +…

A: Given Pr=t0+r-11∆t0+r-12 ∆2t0+r-13 ∆3t0+r-14 ∆4t0+r-15 ∆5t0               (i) To differentiate up to…

Q: 5. Solve Bessel function Jo! xý +y + xy =0, yCI)= 0,7652 ýu) = - 0.44 , h-o.5 (do five iterations)

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Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: Use calculus to solve Eq. (1.21) for the case where the initial velocity is (a) positive and (b)…

A: Givent = 0 to 12s at intervals of 2s.zero velocity occurs at t = 3.470239smotion of the free-falling…

Q: (a) Prove that Σ³ = n²(n+1) ². j=1 (b) Evaluate fr³ de directly from the definition, without using…

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Q: Show that the Fourier series of frx)= x² in El, 1] is x2 (-19^ 4 CosnTx, and hence show that n2 n=}…

A: Given function is fx=x2 in -1,1. We have to show that the Fourier series of fx=x2 in -1,1 is…

Q: Calculate the Fourier series expansion of the periodic function depicted in Figure 2

A: Introduction:The Fourier series representation is a very important infinite series representation of…

Q: Consider Newton's method applied to the function x² + y? – 1 x² – y? – 1 f (x) := Prove that the…

A: As pwe the question we have to prove that the rate convergence of x is quadratic and that of y is…

Q: 9. If a, =1.57, a, -(-1) -11. b, --)" f(t) and period f(t) =f(t+4) up to n=2 is then the Fourier…

A: Fourier series of the function

Q: 11.1.5 Show that (a) cosx = Jo(x) +2(-1)" J2n (x), n=1 (b) sinx =2)(-1)" J2n+1(x). n=0

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Q: Pls solve this question correctly instantly in 5 min i will give

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Q: Siven the following: 00 5(-1)"x2n '(-1)"x²n cos(x) = for all x E R (2n)! n=0 ) Find a power series…

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Q: Consider the periodic function defined within one period by the formula: P(x)=x+ / - (x+1)* if - SXS…

A: Given:The periodic function is defined as  if .To Find:(b)(i) Present the first four terms of the…

Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

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Q: nx) in the E 2n is

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Q: Q/Determine the Fourier series of the periodic function whose definitions in one period is? %3|

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Q: The graphs of y = 1/x and y = 1/ln(x) are shown at right. 2.0 15 a) Set up fully, but do not…

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Q: 0 1 We know that the integral dx Select an answer 5 40 1 If we make the observation that 1 what does…

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Q: 9- a) b) C) e) The Fourier series of the function f(x) + 2 8 0 -4 = 8, -4, -π<x<0 0<x<T at the point…

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Q: Example: Find Fourier series of the periodic functions sinx RCx)= くメくて ○く×くT %3D TTくメく2T

A: Solution for some periodic function f(x) with period T, its fourier series equivalent is given as…

Q: f (x) = sin x, 0 < X < T Express the double expansion of the function, a) with the formula.Plot the…

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Q: Which of the following is Newton's method formula with the correct initial condition to find the…

A: The given problem is to find the initial condition to find the root of the given function by using…

Q: 9. Solve the following equation. sec x - 2 -0 A) 元 x -+ 2n and x- 2n7, where n is an integer 6 B) x…

A: Given: sec x-2=0