Comparison theorem for improper integrals.
With proper integrals, we don't have to worry about whether the answer is actually finite; it is. With improper ones sometimes we can't calculate them exactly, but we still want to know the answer is finite. The comparison theorem lets us do that; it's much more important than in the proper-integral situation.
9.1 Diff-eqs.
We just started this, and solved y' = y/x (the solutions are straight lines through the origin, which makes sense).
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