Prove that the Lagrange's formula can be put in the fom ø (x) f (x,) n P „(x) = Ë Σ %3| r= 1 (x- x,) ø' (x,) | where (x) = II (x- x,). r= 0

Q: 2b. Determine the solution of the following problem using the concept of derivative and integral…

A: The given problem is to find the Laplace transform of the given integral term function.

Q: az az Use the chain rule to find and as at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az %3D…

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Q: Solve the IVP using Laplace transforms. x(0) = 4 15. x'(t) = t², %3D %3D

A: Here we will use Laplace transform method to solve the differential equation.

Q: 1. At z = 0, the function f(z) = z ez has O a. A non-isolated singularity O b. An essential…

A: The function f(z) = ze^1/z has the only singular point at z=0 .  We will use the Laurent series of…

Q: n! Prove that L(t") sn+1

A: we have to show that                                                       Ltn=n!sn+1 we know that,…

Q: 11) Consider F(x) = S*sec t tan t dt a) Integrate to find F as a function of x b) Demonstrate the…

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Q: Consider the function f(x) = In(x). %3D 2.1 Show that x(lIn(x) – 1) is an antiderivative of the…

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Q: 15 Solve the IVP using Laplace transforms. x'(t) = t, x(0) - 4

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: dx Q1/ By Laplace transforms, solve the equation 3 dt - 4x = sin2t given that at t=0, x= 3

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Q: Use the Laplace transform to find the solution f(x) of the following initial value problem for an…

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Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t,    y(0) =…

A: Given :y'' − y' = et cos ty(0)=0, y'(0)=0

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = cos 4x

Q: Let lj,n(x) be the Lagrange polynomial in the formulation Pn(x) = y;l;n(x), j=0 show that for any n…

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Q: 10. Show that the function f(x, y) = e-2y cos 2x satisfies the Laplace equation.

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: Suppose a spaceship of length Lo is traveling at a high speed v relative to an observer. To the…

A: topic - functions

Q: Question 3

A: Q - 3 Recall the approximation: if x = x0 + Δx then f(x) = f(x0 + Δx) = f(x0) + Δx.f'(x0)

Q: of a slab of thickness t and with thermal conductivity k is The temperature gradient, given by de =…

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Q: Q1 (a): Use the Laplace transform method to solve generalized Abel integral equation u(t) dt , f(x)…

A: Given :- Use the Laplace transform method to solve generalised Abel integral equation, fx = ∫0τ…

Q: 1 Prove that L(sinh t) %3D (s2–1)

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Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: 1. Find the tangent line approximation T to graph of f at the given point. f(x) = Vx, (2, vZ) 2.…

A: Since we can only answer one question. We'll answer first question because exact one wasn't…

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: 1. Prove that a. a L{sin at} = a²+s² b. Find Laplace transforms of the followings i. sin 3t + e2t…

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Q: 2s Prove that L(t sin t) (s²+1)2

A: Some Laplace transform formulae: L(tn f(t))=(-1)n F(n)(s) Where Fns denotes the 'n-th derivative '…

Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: Prove f(x,y)=ln(x2+y2)1÷2  by laplace equation

A: Given: The function, fx,y=lnx2+y2 and the Laplace equation, ∂2f∂x2+∂2f∂y2=0.

Q: 2. Find the doivetives of the folloving usina the Differential Operator D. Ans. a) De(x In x) c) D…

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Q: Let L(z) be the linearization of f(x) = sin x + 1 at the point x = . Find L(1/2). O -1 pi/2-1…

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Q: Use the Laplace Transform method to solve the following IVP. y" - 2y + y = cos(t), y(0) = 1, y'(0) =…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Solve the initial value problem using Laplace Transforms. x" - 3x' + 2x = t; x(0) = x'(0) = 0 %3D

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: 10. Show that the function f(x, y, z) = e³x+4y cos 5z satisfies the Laplace equation.

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Q: (a) Solve : 2. at given that : u (0, t) = 0 u (5, 4) = 0 u (x, 0) = sin (xx) using Laplace…

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Q: Q2: Show that the functions satisfies a Laplace equation: (1) f(x, y) = e-2y cos 2x (2) f(x,y,z) =…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Water is leaking from a circular hole(in the bottom) whose area is Ah. When water leaks…

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: Given this periodic function: f(t) =1 from 0<t<a and f(t) = 0 from a <t< 2a Solve for the Laplace…

A: Please find attachment for the details solution

Q: Q2:- a. b. Let u=x²-2xy + 2y³ with x = s²ln t and y = 2st³. Find au/as and au/at. find the total…

A: We need to solve the two questions.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We have to find a linear differential operator that annihilates the given function.

Q: 2. Using Laplace transform to solve y' + y = sin(t), y(0) = 1. %3D

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Q: 10. Show that the function f(x, y) = e=2y cos 2r satisfies the Laplace equation.

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Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: H.W.: prove that the following examples are satisfy Laplace equation 1- f(x,y) =(e-2y)Cos2x 2- f(x,…

A: we have to find which of the following satisfy the Laplace equation.