Question 6 of the Unit 1 exam supposes f satisfies:
f(x+y) = f(x) + f(y) + x^2y + xy^2
It also supposes (A) the limit of f(x)/x as x nears 0 is 1. It says to evaluate f(0).
The solutions says that if A, then (B) the limit of f(x) as x nears 0 is 0. I see that given B, f(0) = 0, but how does A get you to B?
It seems more obvious that since
f(0+0) = f(0) + f(0) + 0^2*0 + 0*0^2,
it has to be that f(0) = f(0) + f(0),
but then f(0) = 0.
It is clear how to go on from here, can someone explain the connection between A and B?

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