# How does one prove this statement or provide a counterexample?

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Is it possible to prove the following statement or provide a counterexample function for the following statement?

Thanks in advance.

#lim_(x->-oo)(f(x))=lim_(x->oo)(f(-x))#

Is it possible to prove the following statement or provide a counterexample function for the following statement?

Thanks in advance.

##### 1 Answer

It's true.

#### Explanation:

Technically, there are cases to be considered when

Assume

Let

Since the limit is L, then there exists an M such that whenever

Now examine

Whenever

For such y, given the above information,

Let

Then there exists an N such that when

This is the definition of the limit on the right side.