Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi

Q: Find the transform of the function below. j(t) = 3sinh(2t)+3sin(2t) A 6/(s^2 - 4) + 6/(s^2 - 4) в…

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Q: Find the Laplace transform of the function

A: The Laplace transform of the function is represented as or , it is defined as , since the…

Q: If z = x + jy, then O Check whether the function f(z) : 1 is an entire function. State the reasons.…

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Q: Get the derivative of the function. Write the final answer in x+jy form 22-9 22 + 1 20z j20y…

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Q: Find the laplace transform of (b) L-- [tan-" )]

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Q: Z (² - -/-) (² - -/-) (2-

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: Illustrate Divergence in three Dimensions?

A: Divergent vector field. Three-dimensional vector field used to illustrate fluid flow with positive…

Q: F(x, y, z) = yzeX²i + e×zj + xyexZk, C: r(t) = (t2 + 1)i + (t² – 1)j + (t² – 4t)k, %3D 0 <t< 4 (a)…

A: Given,

Q: Letf :Z→Zbedefinedbyf(x)=x^2 +1,and letC ={1,2,3}. Find f (C), f ^−1(C), f ^−1(f (C)) and f (f…

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Q: Calculate Vf when f 3x z-y7+ 4x'y+ 2x - 3y-5 at the point (1, 1, 0).

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Q: Find Fourier transform for f(t)=t^3-2t

A: Given function f(t)=t3-2t. To find Fourier transform of f(t). By property of Fourier transform,…

Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: 1 f(z)=- (r+,2) +4)

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: -2x jika x > 0 jika x <0 f(x) =

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Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

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Q: Sow that 2 x² + y² + z² - c²t² is Lorentz invariant.

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: f *g =g *f , where (*) is the convolution in Fourier transform. Select one: True False

A: Given: (*) is the convolution in fourier transform. To prove:  f*g=g*f. Proof: It is known that…

Q: f" > 0 on (-∞, -1) U (-1,0).

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Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

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