Determine which of the following sequences have Fourier transforms which converge: a) x[n] = 2^u[n] b) x[n] = 2¹u[−n] n c) x[n] = (¹) u[n]

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

A:

Q: 1) Does cos" cn) Sin*™(n) converges uniturmly on D, : [0, K14] ?. And on

A: Given sequence of function is, fnx=cosnxsin2nx. It can be written as, fnx=cosxsin2xn. If common…

Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: If this is a left Riemann sum, then *

A: When the rectangle touches the curve with its top-left corners. This is called a left Riemann sum.

Q: te s cosh 7t dt ? L[t cosh 7t] L(te* cosh 7t) O A.) О в) L[cosh 7t] L(e- cosh 7t) C.) D.)

A:

Q: 5a) When p is a real number greater than 1, it can be shown that the improper 1 1 integral |dx…

A: Convergence of Improper Integrals at left-end point: Let us suppose that x=a be the point of…

Q: The limit of n tan(-) as n-∞is equal to 1

A:

Q: Prove that the follo wing series is convergent for all reR Sin Inr) N=1

A:

Q: Use a Taylor expansion around 'a' to prove that In x = In a+x=1 a)". Discuss all the cases of given…

A: Introduction: The Taylor series expansion is an application of successive differentiation. The…

Q: Prove that Hence deduce that L{x"; p} r(n + 1) pn+1 " if n>-1, p > 0. L{x-¹/2; p} = √√(π/p),p> 0

A:

Q: Evaluate O - f 1 1+¹/3+C 0 3 O dx 1+x¹/3 2²/3 In 1+¹/3+C 0 3 - 3x¹/3+3 In 1+¹/3+C 222/3 ○ In 1+¹/³+C…

A:

Q: Find the Z-transform of the following sequence/function (with ROC). Show complete solution.

A: Z-transformation is a discrete transformation of signal. Through the Z-transformation, one can…

Q: Q.3. Find the fourier expansion for the function whose definition 一T х, (x) = 0, くxく- 2 <x< -

A: Given that function we have to find the Fourier series of that function.

Q: Evaluate (1+¹/2 - 10+3/2) dt using the Fundamental Theorem of Calculus, Part 2. 15 [¹³ (1t1¹/²2 -…

A:

Q: Q2\ Determine the z transforms of the following sequences *

A: In the given question, the concept of Z-transform is applied. Z-transform In its most basic form,…

Q: Which of the following is equal to cosh(In x)? 2+1 A)국 (B)군 2x 2x (C) (D) (H) 2x + 1 2x 2x

A:

Q: L { cosh It

A: A Hyperbolic function is given.

Q: is x^4+1 irreducible in Z_2[x]?

A:

Q: 3) Find L{2re*} using two methods.

A: One method is by using formula and derive whole solution. 2nd method is direct method by using…

Q: Approximate the area under f(x)=3x^2 +1 on [-5,0] using RIGHT Riemann sum with 5 approximating…

A: According to question,Given Function,f(x)=3x2+1,In the interval -5, 0

Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t&gt;0=0, t&lt;0 Therefore,…

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: Prove that Q_n = sup 1/n(1-(1/(nx+1))=1/n

A: Answer

Q: 26) ) Show that the reductión formula for 1ー2 Sec" ndx = Sec atan n t n-2 n-- n-1 ) Hence use tta…

A:

Q: f(x)= == ¹xcl! Obtain the Fourier transform of

A:

Q: y' + y" = 2x²y 10y' - y = ex 2 tanh(y)y′ +2xy+3=0 y” = tanh(y/x)

A: To define whether each of the following ODEs are 1st-order linear, 1st-order non linear,2nd-order…

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: pefficien

A:

Q: 4. Evaluate [(3x? - x + 6)dx i) 1 + 1(1? +1)' ]dt ii) o V1 +x* iii)

A: 4 (i). Given integration is : ∫-133x2-x+6dx To find the value of integration.

Q: 2 Construet a tnuth foble for FPv (avs )]^ [-RV(Qvs]] P>A1(eAR)]=> (R=>P)

A:

Q: let Fx) = ーn, -H<X <〇 /0くx<H find the Fourier series of F(x) over [-I, M] [-M, H]

A:

Q: B2. Euler's Theorem Let G = U(n) %3D Prove For any a in G, a^m = 1 (mod n), where m = (phi) (n),…

A:

Q: Exercise 2. Let f be the 27-periodic function defined by f(2) = Then A) the Fourier series of f is…

A: Here we use the following fact to answer the question:  If f(x) is a piecewise smooth on the…

Q: Let xfn] be a discrete-time signal whose Fourier transform between -r and r is 4 |w< 4 X(e) = 0, 4…

A: Given Discrete time signal xn whose Fourier transform between -π and π isXejw=4πw2,  w&lt;π40,…

Q: (e) Choose {X,}"-1 from [0, 1]. Let p, be the probability that X; + X;+1 < 1 for all i € {1,2, ., n…

A: Given thatXi for i = 1,2,3,...,n are distributed uniformly from 0,1. Let us consider two random…

Q: Consider following ODES: 1)4y" +12y' +13y=0,2 a) Find characteristic equation ar

A:

Q: Apply integration to the expansion 00 E(-1"x" = 1 – x +x² – x³ + ... 1+x n=0 to prove that for -1 <…

A: We can represent a series in the form ∑n=1∞ anx-cn where c is the centre of the series and ai is the…