# How do you determine the limit of #(x² - 3x - 2)/(x² - 5)# as x approaches infinity?

Given,

Divide every term by the term with the highest degree in the denominator.

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To determine the limit of (x² - 3x - 2)/(x² - 5) as x approaches infinity, we can divide the numerator and denominator by the highest power of x. This gives us (1 - 3/x - 2/x²)/(1 - 5/x²). As x approaches infinity, the terms with 3/x and 2/x² become negligible, and the limit simplifies to 1/1, which is equal to 1. Therefore, the limit of (x² - 3x - 2)/(x² - 5) as x approaches infinity is 1.

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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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