# What is an example l'hospital's rule?

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An example of l'Hôpital's rule is when you have a limit of the form 0/0 or ∞/∞. For instance, if you have the limit of (x^2 - 4)/(x - 2) as x approaches 2, you can apply l'Hôpital's rule by taking the derivative of the numerator and denominator separately. In this case, the derivative of x^2 - 4 is 2x, and the derivative of x - 2 is 1. Then, you can evaluate the limit of the derivatives, which is 2, to find that the original limit is also 2.

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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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- What are the asymptotes of #f(x)=-x/((x^2-8)(5x+2)) #?
- How do you prove that the function #x*(x-2)/(x-2)# is not continuous at x=2?
- How do you find the limit of #(1+(7/x)+(3/x^2))^x# as x approaches infinity?
- Evaluate the limit # lim_(x rarr oo) (2x - sinx)/(3x+sinx)#?

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