Green's Theorem as a Fundamental Theorem of Calculus Show that if the flux form of Green's Theorem is applied to 'f(x) the vector field (, 0). where c > 0 and R = {(x, y): a < x s b, 0 s y s c}, then the result is the Fundamental Theorem of Calculus, dx = f(b) – f(a). x

Q: Prove or disprove that if ∇ . F = 0 and ∇ * F = 0, then F = 0

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A: Given Q and Z are vector valued functions such that:Q-1=0,0,-2Q'-1=1,-1,-1Q''-1=3,2,-2 and…

Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

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A: Please see the below picture for detailed solution.

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Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

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Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

A: TO solve the question, we use the following facts (a) A functions is differentiable at a point if…