# How do you evaluate each of the following limits, if it exists #lim (3x^2+5x-2)/(x^2-3x-10)# as #x-> -2#?

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To evaluate the limit lim (3x^2+5x-2)/(x^2-3x-10) as x approaches -2, we substitute -2 for x in the expression. This gives us (3(-2)^2+5(-2)-2)/((-2)^2-3(-2)-10). Simplifying further, we have (12-10-2)/(4+6-10). Continuing to simplify, we get 0/0. This is an indeterminate form. To evaluate the limit further, we can use algebraic manipulation or apply L'Hôpital's rule.

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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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