If we are told that the integral$$\int f(x,y)dx$$converges, then can we say that$$\lim_{y\to0}\int f(x,y)dx = \int \lim_{y\to0}f(x,y)dx$$?If this isn't enough information, what do we need to know in addition about $f$ in order to be able to move the limit inside the integral?
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