For the following function f:R3 → R2 x?yz x² – y) f(x,y,z) = {(x2+ y² + z²'1+z² )• x,y, z) # (0,0,0) (0,0), (x, y, z) = (0,0,0) i) Determine if it is continuous at the origin of coordinates ii) Determine if the Jacobi matrix exists at the point (0,0,0) iiI) Determine if the nparcal derivatives of each of the components of the function are continuous at the origin iv) Determine if the function is differentiable at the origin.

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A: h(x , y) = g∫(x, y)g(t) = t +In t∫(x, y) = 1-xy1+x2y2∴h(x , y) =g 1-xy1+x2y2⇒h(x , y) =1-xy1+x2y2 +…

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Q: B) Integrate f over the given region 1. Square f(x, y) = 1/(xy) over the square 1 ≤x≤ 2, 1≤y≤2 2.…

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