If F = Za[z] (z²–cz+1) find the value of c for which F will be a field? %3D

Q: Evaluate fSS, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

Q: Find the Fourier expansion of f(x) = 3–x ; 0<xs 2n; |D

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Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0

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Q: If Osf(x)s g(x) on [a, ∞) and | g(x)dx is divergent, then | F(x)dx is divergent. Select one: O True…

A: We have to state true or false.

Q: dr and dz both diverge when p = O a O b O c -1 O d 0.5 O e 1 2.

A: If the limit of integration fails to exist, then the improper integral is said to diverge.

Q: Use Laplace transforms to solve the following initial value problem. x"-25x 9t; x(0)=x'(0) = 0 %3D

A: Given: Given IVP is x''-25x=9t,x0=x'0=0 To find solution of IVP we use Laplace transform

Q: What is the inverse transform of F(s) = In (s'/Vs2 +4s +5}

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Q: Let R be and bl#0) = iff a with unity - Let a l#0) in R- Show that and b an I.D are are associates-

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Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: a k 2 + k² S 2 + k² k

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Q: x* 2 2 xzəz = (+)1-7 o + 12 s-2

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Q: Find a potential function f for the field F. F = (5y + 2z)i + (5x + 3z)j + (2x + 3y)k A general…

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Q: 4xy V = -2xz XZ

A: relationship between voltage (V)  and uniform electric field (E) can be given by  E→=-dVdr=−∇→V…

Q: FIAD THE OTER FIXF FUH aiON OF ĦF xauTF XHGUE X O SIn X =3

A: The given function is:sinX=35To find other five function

Q: Solve the PDE u + 2xtu,=u²; *ER,t> 0 by reducing it to an ODE using an appropriate choice of…

A: As per the question we are given the following first order PDE : ut + 2xtut = u2  ,  x ∈ R , t &gt;…

Q: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

Q: Chose the Fourier expansion that reduces the length of the solution for the functionf (x): f(x) =…

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Q: A sufficient condition to use Newton's progressive formula for inclusion is: Xnxo (A) m = |m| < 1 n…

A: Solution:-

Q: b. x" — 6х' + 8х 3D 2 x (0) %3D 0 аnd x'(0) %3D 0

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Q: Find a potential function f for the field F = ev *2=(4 i + 4x j + 8x k). A general expression for…

A: We can calculate the following question by usual method of calculating potential function

Q: Solve the following problem given that the scalar field f = xy? + 3xiz². Find Vf at point (8,1 -2).…

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Q: what is the Fourier transfrom of the following 0.5 d²x(t) j2nf dt2

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: the potential function f for the field F = 5x i + 9y j + 4z k. eral expression for the infinitely…

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Q: show that: n L{t"-1eat} S - a L{t"eat} By using the definition of the Laplace transform

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Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

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Q: (d) Show that the Fourier transform of a Gaussian is a Gaussian, and hence show that eik dk 2πδ(x).

A: The Dirac delta function is one of the most significant functions in mathematics. It is widely used…

Q: Consider the function S e20x+2, if x 0 The Fourier transform of f, defined by F(f)(§) := f…

A: Integral 0 to infinity the function must be zero. So only - infinity to 0, the integral exist.

Q: O y" -3y' + ay = e*

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Q: Find the value of Uhe detorminant OF A using lhe tollowing me toods! Laplace Expansion 4 2 3. A = 3…

A: We need to find the determinant of matrix A, using Laplacian expansion.  A=242353442232 The order of…

Q: Which of the following is homogenous of smallest degree? x4+y4 A x-y B Vx-y x-y x+y D In x – In y

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Q: (b) What is the Fourier Transform of x?8(x² – a²)?

A: The given problem is to find the Fourier transform of the given function, in the given function…

Q: No. B Diagram 1 OF the Field IS &m more than tS wkith, The iength Ae Given that the area OF the…

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Q: Find a potential function f for the field F. F= (y + 5z)i + (x+2z)j + (5x + 2y)k ..... A general…

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Q: -et Cos wot Z a tj w 2 t Wo

A: We have to use Fourier transform formula.

Q: Which of the following graphs is the slope field for 15/1 1~/1ST ~\~ in 13t-ii-i ~~~ -1 1 2 3 4 5…

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Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0 Thanks

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Q: Q6. Let C[0,1] have the inner product < f,g 2 S,"f(x)g(x)dx and let fn= cos nx (n=0,1,2,3,....).…

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Q: Defn `x;>-` "x; diverges to minus infinity" VR>O such that Vj >Ng *;<-R NR HWs If x→0 then → O.…

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Q: Solve the following problem given that the scalar field f = xy? + 3x3z?. Find Vf at point (8,1, -2).…

A: Given function is, f=xy2+3x23z2  Now, calculating ∇f…

Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: Q2/ Find the Fourier expansion of the Periodic function whose de finition in one Aeriod is : Fo =…

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Q: Find the Fourier-Hermite expansion of f(x) = x³, x E R.

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Q: Ex Using Cramer's Rule to solve the sys x-y+z 0 2x +y-3z = (x+y+z%3D

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Q: Q2= A) for E- 2x1-3Y3+K prove That div( curl È)=0 B Find A and M if (21+bj+27k) X (i+Ai+Mk)=0 I uck

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Q: 5. Use the Laplace Transform solve the IVP: x' + y = t (4x + y' = 0 x(0) = 1, y(0) = 2

A: Theory : The Laplace transform of a second order linear differential equation : y" +α y' +βy =f(t)…

Q: Find the inverse Laplace of  (s+1)/(s2 -3s +2)

A: With the use of partial fraction we did this question.

Q: find all x EIR such that 1z +zl + lz - loog | = (2+ 2015)

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Q: Show that (A − B)T = AT − BT .

A: We have to use the properties of subtraction of matrices and matrix transpose operation. In matrix…

Q: dy = x - y with possible particular solutions Y1, 42, Y3 and y4 sketched onto the slope field. Which…

A: Given the differential equation dydx=x-y. It's slope field has 4 possible solutions.  The best way…