(1- 2xt + t?) = (x-t)(x,t) (1) at ag (1- 2xt + t) t g(x,t) (2) ax ag t= (x - t) ag at (3) ere g(x,t) is the generating function of Legendre's polynomials Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P-n Pn-1

Q: 3) Find Fourier series expansion of he funchion f(x) - T/2 Śn 2o %3D cos n

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Q: Estimating In(1.4) using a Taylor polynomial about a = 1, what is the least degree of the polynomial…

A: fx = lnxTo estimate : ln1.4  using Taylor's polynomial centered at a=1. To find the least degree of…

Q: 59. Partial fraction decomposition shows +号This (x-a)(x-b) In|+c. dx can be used to show ƒ ¤--b) =…

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Q: solve the recurrence relation with the given initial condition.

A: y1 = 1 , y2 = 6 , yn = 4yn-1 - 4yn-2 for n ≥ 3 y3 = 4y2 - 4y1 = 24 - 4 = 20 y4 = 4y3 - 4y2 = 80 - 24…

Q: 1-x 1 0 0x=x-7x denklemini sağlayan x değerlerini bulunuz. 21 -1 X 4

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Q: xample 8.19. Use Romberg's method to compute ax correct to 4 decimal places. 2 0 1 + x²

A: Solution :-

Q: 25: Using a suitable Fourier- Series expansion for 0 S x ST: A) Show that: x(n -x) (cos 2x cos 4x .…

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Q: Find the Fourier series (ao, an, bn and the fourier series formula) f(x) = {0 if − 2 < x < −1 f(x)…

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Q: Find general solutions in powers of x of the differential equations in Problems through. State the…

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Q: A. Find the Fourier Series af x)= -x- = X+Y 0 4x<

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Q: 2--solve the Fourier series for the function f(x) = 3- x ,and -n < x < T. A:f (s) =+E-1 4(-1)"Tsin…

A: Concept:

Q: To find v,(x=0.1) yn-1-0.1+ (0.1)2-1(0.1)" +급(01).-0.909675 To find y2(x=0.2) Expansion around x0 HW…

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Q: Example 6. Find the Fourier series for the function f (x) = 1, -1, if -n < x <- if - <*< if < x < T…

A: The following is the given function:   fx=-1,if -π≤x≤-π20,if -π2&lt;x≤π21,if     π2&lt;x≤π It is…

Q: Example 2: Find the Fourier series -1, f (x) = 1, f«) = - 1< x < 0 0 <x < 1

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Q: 5- Find the fourier series of function below: - n< x < -n/2 - T/2 < x < 0 0 <x < n/2 1/2 < x < n -2…

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Q: A continuous periodic signal x (t) of real value y has a fundamental period of T = 8. The…

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Q: 4. Use partial fraction expansion to find x[n] for the following function: 3z-1 X(z) = Iz| > 2 %3D…

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Q: In (1tel function a-0 what ore the first four terms of the taylor serial Yotation o+

A: Given function is fx=ln1+ex and center a=0. We have to find the first four terms of the Taylor…

Q: 3. The Chebyshev polynomials of the first kind are defined as Tn(x) = = cos (n arccos(x)) (b) Show…

A: in the given question we have to prove that the chebyshev polynomial Tn(x) = cos(ncos-1(x)).…

Q: blem 5: Suggest a polynomial on [0, x] whose Fourier coefficients decay as rapidly as and confirm…

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Q: 7. Let f(x) = In x and n E N. %3D (a) Show that the Taylor polynomial п ▪(-1)k-1 Pn := Pf.1 -(x –…

A: Step:-1 The Taylor Theorem with Remainder of a function f(x) around a is f(x)=f(a)+…

Q: Find the n-th Taylor polynomials for f(x) = e-x about x = ln 2 and express it in sigma notation.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (a) If f(x) is a periodic function of period 2n and if f(x) = x* %3D in the interval -T, T find its…

A: fx = x3,period : 2π,Interval : -π, π

Q: [2, if - 2<z < 0 1, if 0 <r< 2 3. Find the fourier series expansion for f(r) = and show that 1 ( a)…

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Q: 2. Find the Taylor series of g(x) = at x = -1.

A: 2. g(x)=1x5 at x=-1

Q: Use method of undetermined coefficients to find the solution of non-homogeneous Fi- bonacci…

A: The associated homogeneous recurrence relation is

Q: 28. Let f be a function that has derivatives of all orders for all real numbers, and let P3(x) be…

A: let f be a function that has derivatives of all orders for all real numbers , and P3x be the third…

Q: 1. Find the Fourier series of the function -x if -4 <x<0 f(x) = S(x + 8) = f(x) if 0<x<4

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Q: 1.)Determine whether the Fourier series of the following functions converge uniformly or not. a.…

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Q: 1;0<x<1 f(x) = {2 – x ;1 <xs2 (Fourier series) Then b, =0 اختر احدى الدجابات True False

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Q: Let y" + 2xy = 0 Find general solution for y(x) as a series y(x) = > Anx" n=0 Show the recursion…

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Q: Suppose that the growth of a population of bumblebees follows the recursion model, Pt+1 =a Pt when…

A: The given model is a time series model or more specifically it is an auto regressive model of order…

Q: Find the exponential generating function F(x) for the numbers fn of forests on vertex set [n] having…

A: Given below clear explanation

Q: 5- Consider the following finite difference approximation Uij+1-Uij * (ui+1, - 2u., + ui-1,) +(4+1,…

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Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: 5. Find the inverse Z-transform of X(z)=242-1 using partial fraction and find first five values of…

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Q: 9.The Laguerre13 differential equation is xy′′+(1−x)y′+λy=0.xy″+1−xy′+λy=0. a.Show that x = 0 is a…

A: From the given equation we have            P(x)= x            Q(x)= 1-x            R(x)= λ The…

Q: The differential equation (x + 1)²y" + (x − 1)(x + 1)y' + 2(x + 2) y = 0 has a series solution of…

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Q: Find the expression for F(z) while solving the recurrence relation 2yk+2 − 3yk+1 + 7yk = ka k by…

A: Recurrence relation given to us is2yk+2-3yk+1+7yk=kak.........(1)Let Z[yk]=Y(z)We take Z transform…

Q: Which A and B satisfies the general solution A2" +B3" of the second order linear homegeneous…

A: See the detailed solution below.

Q: -4 -3 -2 -1 At t = 7, the Fourier series of f converges to the value of %3D

A: According to the graph, the function f(t) is a piecewise smooth on the interval, -4≤t≤4. Since the…

Q: 2. (a) Define a Dirichlet function. (b)Assume that f(x) is a function of the form -х-1%; when -7 <…

A: 1st we will defined dirchlet function and then check given function satisfies its condition or not .…

Q: 4. Let F(n) = 2F(n – 1) + 5F(n – 2) – 6F(n – 3) with initial conditions F(0) = 4, F(1) = -4 and F(2)…

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Q: Q.x2(x2+1)y′′+7xexy′+9(1+tanx)y =0

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Q: The zeros in the given matrix make its characteristic polynomial easy to calculate. Find the general…

A: Concept: The general solution of the matrix is given by x(t)=c1x1(t)+c2x2(t) Wherex1 and x2 are two…

Q: (x-2, – 2, -5<x<0, 19. f(x)=- [1, 0 <x<5.

A: To find the Fourier series expansion of the function: fx=x−2   −5&lt;x≤01   0&lt;x≤5 Note that the…

Q: 3. Let F(n) = 9F(n – 1) – 24F(n – 2) + 20F(n – 3) with initial conditions F(0) = 1, F(1) = 5 and…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: 3. Find the Fourier series of, - n<x<-1/2 f(x) = }0 - 1/2 <x <n/2 1/2 < x <n 1

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Q: 334 In attempting to solve a simple PDE, a system of finite-difference equations of the form u+1 =…

A: