Is the following function continuous at the point 0 0

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11.Is the following function continuous at the point(0,0,0)?f(x, y, z) =xy+yz+z2x+y+z2(x, y, z)6
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Partial Derivatives1.Letf(x, y) =exyx2+y2. Computefx(x, y)andfy(x, y).
2.Letg(r, θ, z) =r2cos 2+zrθ-2r-z. Computegz(1,π4,2).
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3.Joe just bought an Old Fashioned Buttermilk donut and a Valrhona Triple Chocolate donut from Fire-cakes, and is trying to decide which one to eat first. After extensive testing and data collection, Joe hasmodeled his happiness as a function of consumption of donuts. LetHdenote happiness,Bdenote thenumber of Old Fashioned Buttermilk donuts consumed, andCdenote the number of Valrhona TripleChocolate donuts consumed. ThenH(B, C) =e3B+ (B+ 1)(C+ 1)3+eC2If Joe only has time to take a single bite of one donut, which one should he eat?

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