Prove the following: Let f and g be real-valued functions defined on (a, infinity). Suppose that...

Prove the following:

Let f and g be real-valued functions defined on (a, infinity). Suppose that lim{x to infinity} f(x) = L and lim{x to infinity} g(x) = M, where L and M are real. Then lim{x to infinity} (fg)(x) = LM.

You must use the following definition: L is the limit of f, and we write that lim{x to infinity} f(x) = L provided that for each epsilon > 0 there exists a real number N > a such that x > N implies that |f(x)-L| < epsilon.

Expert Solution

Colby Messinger answered 8 months ago

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