# 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.

It's true.

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To prove a statement, one typically uses deductive reasoning, starting with known facts or accepted principles and logically deriving the conclusion. A proof involves a series of steps, each justified by a previously established fact or logical rule.

To provide a counterexample, one needs to find a specific case where the statement is false, thereby disproving it. This involves finding a specific instance that contradicts the proposed statement.

In both cases, clarity and precision are key. The proof should be logically sound, with each step clearly justified, while the counterexample should be specific and clearly demonstrate the falsity of the statement.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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