Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz., F-1{F(w)}=f(t)=T2.

Q: 5. Apply the eigenvalue method to find the general solution of the given system. Find aiso the…

A:

Q: IExample 6.9. One entry in the following table is incorrect and y is a cubic polynomial in x. Use…

A: The problem can be solved by making difference table.

Q: Use the Solovay-Strassen test to show that 7739 is composite.

A: Given Number is 7739 To show that 7739 is composite using the Solovay-Strassen test. Euler…

Q: Solve by D operator method dx2 d'y 20 dx +y = x2e3*.

A: We have to find the solution of given differential equations.

Q: 6. Which is is true for any set S of real numbers? * S has a least upper bound. S has a greatest…

A:

Q: What is the chromatic number of the given graph?

A: We have to find the Chromatic number of the given graph.

Q: Determine whether the statement is true or false. In R3 the graph of y = x2 is a paraboloid. O True…

A:

Q: Proof of CRT (for two moduli) We must prove that f: Zm,ma Zmx Zm gimern by is a bijection.

A: We shall solve this using various properties of GCD. The detailed typeset solution is presented in…

Q: Let -1 -5 -3 14 -8 -1 A = 1 -2 16 2 -13 -13 -3 Find orthonormal bases of the kernel and image of A.…

A:

Q: Example 6.13. Prove that ge + 8 1+ 4 (i) A (ii) 1 + 8°µ? = | 1+ : 2+A 1 1+ 4 (iii) u = 2V(1+ A)

A: Please find solution below:

Q: Bruijn graph and identify an Euler path hence -mbling the original sequence from which they e…

A: Sol

Q: (cos 20+ jsin 20) (cos 60+ jsin 60)1" (cos 30+ jsin 30)°(cjs 1000)

A: the given expression is cos 2θ+jsin 2θ5cos 6θ+jsin 6θ10cos 3θ+jsin 3θ9cjs 10θ Using De Moivre's…

Q: 5. Help Aunt May in answering some problems about independent events. Consider generating a random…

A: Number of possible 3-bit strings is 23 = 8. They are {000,001,010,011,100,101,110,111} Now,  A =…

Q: The Inverse Laplace Transform for 1/S-3 is u(t)e^3t e^-at t^2 t

A:

Q: T(E,)n T(E) = {0} and T(E,) + T,(E,) = F. %3D Show that T(E,) and T2(E2) are closed subspaces, i.e.…

A: Sol

Q: In three dimensions the equation x² + y? = 1 represents a Similarly, the equation y +z = 1…

A: We will answer this question by analysing figures given in the question

Q: 3. 2х, — х, = 2 X - 3x, + xz = -2 3x3 —х, + х, — 3х, — —6 -X, + x2

A:

Q: a cube. a. How many of the remaining nets have these two groups of three in the correct orientation…

A: Sol

Q: 2y+y = x²e 3x. d?y thod - dx2 2. Solve by method of variation of parameter - 2 = ex sin x. %3D dx?…

A: Solution by a variation parameter method

Q: ((V x F)(x)) u = 1 lim r-0 Tr2 F. ds, he circle of radius r in R3 centered at x lying in the plane…

A: Sol

Q: Solve, 9 7 0 3 0 5 - 9 1 3 -8 5 3 -7 5 7 6 2 6 4 0 1 -1 9

A: We have to solve    753-7862  6101-19×-8 9 7   5 0 3   4 0 5-9 1 3.

Q: > ||X(jw)||, where ||x(s)||1 s)[ds and ||x(s)|| = sup|x(s)|. SER

A: Sol

Q: 1. Solve by D operator method dx2 d?y 20+y = x²e3x. dy dx

A:

Q: Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

A:

Q: Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan…

A: We can solve this using formula

Q: Refer to the following theorem: If A is an mxn matrix with linearly independent columns, then A can…

A: Solution

Q: 2. Determine the volume generated about y-4 the area boun ded bay ×キの x and x?ty =3 メ %3D

A:

Q: 2. Using the given pairs of x and f(x), construct a an appropriate table (difference or divided…

A: We have to find f(5) and the equation of the polynomial that will fit the given points.

Q: 5. Fill in the blank: For x, y E R. Equality in the Triangle inequality is satisfied, i.e. [x+y = x…

A:

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS : F(t)= for…

A:

Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y + z)k and the surface z = 4 – x²…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.

Q: m An = {-: m e N}, ne N, n where N are non-negative integers. What is lim inf A, and lim sup A,?…

A: To find the lim sup and lim inf of the given sequence An .

Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

A:

Q: Determine whether the lines L, and L, are parallel, skew, or intersecting. x - 3 y – 2 _ z - 12 1 -2…

A:

Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: Find aw/ar and əw/əs when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs. %3D

A: We have to apply the partial derivatives.

Q: Dêtermine the equation of the circle graphed below. 10 8. -10 -8 -6 -4 -2 2. 4. 6. 8 10 -2 -4 -8 -10…

A: Given: graph of circle

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

A:

Q: Which adjacency matrix could represent this graph? Select one: O A. [1 2 1 1 2 0 2 0 1 2 1 1 [ 0 1…

A: We want to find the adjacency matrix of the given graph.

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

A:

Q: 1. Solve by D operator method d?y 2y +y x2e 3x. dy dx2 dx Solve by method of variation of parameter…

A:

Q: 2m de Question #7) 12 - sin 0

A: q-7) let I=∫02πdθ12-sinθ it is known that  sinθ=2tanθ21+tan2θ2 I=∫02πdθ12-2tanθ21+tan2θ2…

Q: (b) у" — 4у'+ Зу %3D Зе2х + 4е* + 2e3х

A: Given differential equation: y''-4y'+3y=3e2x+4ex+2e3xTo find: General solution of the differential…

Q: + y = x?e3x. dx2 dx d?y 2 dx2 2. Solve by method of variation of parameter dy = ex sin x. dx 3.…

A:

Q: ди y ду ди dx

A: Solution

Q: Find the Inverse Laplace Transform of the following functions 8. 4) F(s) = ,4 4s Ans. f(t) =…

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

Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

A:

Q: a. Show that K5,6 has a path containing all vertices in the graph. b. Explain why K5,6 is not…

A: Hamiltonian graph - A connected graph G is called Hamiltonian graph if there is a cycle which…

Q: Show that if f(n) and g (n) are both solutions to a linear homogeneous recurrence equation with…

A: Let the homogenous linear recurrence equation be        an+1 = k1an + k2an-1 + . . . . . . +…