# What if L'hospital's rule doesn't work?

If L'Hôpital's Rule doesn't work, it typically means that the given limit does not have an indeterminate form of ( \frac{0}{0} ) or ( \frac{\infty}{\infty} ), which are the conditions required for applying L'Hôpital's Rule. In such cases, alternative methods may need to be employed to evaluate the limit. These methods might include algebraic manipulation, factoring, rationalizing, or using other limit properties. Additionally, it's possible that the limit may not exist or may require more advanced techniques beyond the scope of elementary calculus.

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l'Hopital's Rule occationally fails by falling into a never ending cycle. Let us look at the following limit.

As you can see, the limit came back to the original limit after applying l'Hopital's Rule twice, which means that it will never yield a conclusion. So, we just need to try another approach.

by including the denominator under the square-root,

by simplifying the expression inside the square-root,

So, we could come up with the limit without using l'Hopital's Rule.

I hope that this was helpful.

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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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