Evaluate the triple integral I y sin(та4) dV E where E is the set of all points (x, y, z) in 3-space such that 0 < x < 1, 0< y < 3x, x

Q: discuss the continuity of the function. a) f(x,y,z)=z/(x^2+y^2-4) b)f(x,y,z)=xy sin z

A: (a) consider the provided question,   fx,y,z=zx2+y2-4  The given function is continuous except at…

Q: Use the cauchy-riemann conditions to determine whether the function f (z) = ((x ^ 3) + x(y ^ 2)) + i…

A: Cauchy-Riemann  : Let f(z)=u(x, y)+iv(x, y) be a complex valued function. Then the Cauchy-Riemann…

Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

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Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: Let f(x, y) = cos(xev*) + cos(x + ey²) , find дхду* O a. -2ye" (sin(xe") – x cos(xev*) + cos(x +…

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Q: Q\ Let F(x,y,z)=(sin(xy), e",2x+yz") then find: 1. Grad F(x,y,z) at (-1,1,-1) 2. Div F(x,y,z) at…

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Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Show that f(z) = x ² + y ² where z = x + iy is not analytic anywhere using Cauchy Riemann equations.

A: Cauchy Riemann Equations: Given,  f(x+iy)=u(x,y)+iv(x,y)  and it should satisfy  ∂u∂x=∂v∂y and…

Q: Find div F and curl F if F(x, y, z) = 9ei - 3 cos y j + 2 sin² z k. div F= curl F=

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Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

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Q: af of H.W: Find and for the functions: b əx ду 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2)…

A: Given functions are 1. f(x, y)=(xy-1)2 3. f(x, y)=(x2-1)(y+2) 4. f(x, y)=x(x2+y2)   To Find: ∂f∂x…

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

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Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

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Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: integral f t^3 In t dt

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: Determine whether the function f(z)=z^2+(bar z) is analytical at z=1+i, where (bar z) denotes the…

A: Analytical functions, also known as holomorphic functions, are complex functions that are…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: + Find the maximum value of isu = Sinn Siny Sincnty) U

A: The given problem is to find the maximum value of the given function u=sin(x)sin(y)sin(x+y).

Q: Suppose z = f(x, y) is a differentiable function of x and y, x =r cos 0, and y =r sin 0. (a) Compute…

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Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…