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In high school mathematics, how to see whether the function approaches positive infinity or negative infinity and so on.
Necessity: Because limf(x)=Ax tends to infinity, there is a positive number m for any positive number ε, when │ x │ >; M, with │ f (x)-a │.
Sufficiency: since limf(x)=limf(x)=Ax tends to positive infinity and negative infinity respectively, there is a positive number M 1 for any positive number ε, when x >; When M 1, there is │ f (x)-a │.