# How do you find the limit of #(tan^3 (2x))/ x^3# as x approaches 0?

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To find the limit of (tan^3 (2x))/ x^3 as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get 6tan^2(2x)sec^2(2x) and 3x^2. Evaluating these expressions at x=0, we find that the limit is 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.

- How do you determine the limit of #(x² - 3x - 2)/(x² - 5)# as x approaches infinity?
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- How do you find the limit #lim_(x->2^+)sqrt(2-x)# ?
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- How do you find the limit of #(x^3 - x)/(x-1)^2# as x approaches 1?

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