# Lim x−→2 (x^2 − 4) tan(2x − 4) / (x − 2)^2 Find the following limits. Show all steps. If the limit does not exist, explain why not? Not allow to use L’Hospitals rule.

Evaluate the limit:

Note that:

so we can simplify:

Now consider the limit:

that is a well known trigonometric limit:

So:

graph{((x^2-4)tan(2x-4))/(x-2)^2 [-4.873, 5.127, 6.26, 11.26]}

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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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