What is a comparison theorem?

By Forinfos - 23/02/2026 - 0 comments

A comparison theorem is a test of whether or not a mathematical object satisfies a set of predetermined properties. In calculus, a comparison can test if an integral is convergent or divergent. It is useful when one is not concerned with the actual value of an integral.

There are times when it’s not possible to integrate, yet important to examine, the behavior of an integral. For example, if f and g are continuous functions, such that 0 ? g (x) ? f(x) for x ? ?, and function f(x) dx converges, then function g(x) dx converges, and if g(x) dx diverges, then function f(x) dx diverges.

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