# How do you evaluate #\lim _ { x \rightarrow - \infty } \frac { | x - 4| } { 2x }#?

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To evaluate (\lim_{x \rightarrow -\infty} \frac{|x - 4|}{2x}), we consider the behavior of the expression as (x) approaches negative infinity. Since (x) approaches negative infinity, the absolute value of (x - 4) will approach infinity as well. Additionally, since (x) approaches negative infinity, the denominator (2x) will also approach negative infinity.

As (|x - 4|) approaches infinity and (2x) approaches negative infinity, the quotient (\frac{|x - 4|}{2x}) will approach zero, since the numerator grows faster than the denominator. Therefore, the limit is (\lim_{x \rightarrow -\infty} \frac{|x - 4|}{2x} = 0).

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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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