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Answer:
f(x, y) = Sin(x*y)
We want the second order taylor expansion around x = 0, y = 0.
This will be:
So let's find all the terms:
Remember that:
f(0,0) = sin(0*0) = 1.
Then we have that the taylor expansion of second order around x = 0 and y = 0 is:
sin(x,y) = x*y + x*y + x*y = 3*x*y