Why is L'Hopital's rule not preferred for solving limits?

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In summary, L'Hopital's rule is not a favored method of professors and grad students because it is often considered overkill and can be difficult to apply properly. Some suggest using Taylor approximation as a more precise alternative. L'Hopital's rule is seen as a shortcut way of applying Taylor series to solve limits.
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Ignea_unda
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Having read many of the posts on limits over the past year or so (and having been told by a few of the posters) I have come to see that L'Hopital's rule is not a favored method of professors and grad students. Why is this and/or what would I be better spending my time perfecting (for I'm a big fan of L'Hopital's as of now)?
 
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L'Hopital's is quite often "overkill". It works but it is, in my opinion, better to understand how to take the limit than just turn the crank of a powerful machine.
 
  • #3
In my opinion...

The De L'Hopital method is demontrasted to work only under certain Hypothesys that are often hard (or boring) to check.
So, even if it lead to the right result, to be mathematically sure that you could legittimately apply it is a longer procedure than using an alternative method.

I think using Taylor approssimation of a functon to a polinomial is a more precise and worth method and in some way we can consider the De L'Hopital method as a brief and imprecise way of applying the Taylor series to solve indeterminateness in claclulating the limits.
 

1. What are limits in scientific research?

Limits refer to the boundaries or constraints within which a scientific study is conducted. These boundaries may include restrictions in terms of resources, time, and ethical considerations that may impact the scope and generalizability of the research results.

2. Why is it important to set limits in scientific research?

Setting limits allows researchers to focus their efforts on a specific area of study and ensures that the research is feasible and manageable. It also helps to maintain the validity and reliability of the research by preventing it from becoming too broad or unfocused.

3. What are some common methods used to establish limits in research?

Some commonly used methods to establish limits in research include setting specific inclusion and exclusion criteria, defining the population or sample size, and determining the scope and objectives of the study. Ethical guidelines and funding limitations may also play a role in setting limits.

4. How do limits impact the reliability of research findings?

Limits can greatly impact the reliability of research findings. By setting clear boundaries, researchers can control for external factors that may affect the results, making the findings more reliable. Additionally, setting limits can help to ensure that the study is replicable, further increasing the reliability of the results.

5. Are there any potential drawbacks to setting limits in research?

While setting limits is important in research, there can also be some potential drawbacks. For example, setting too narrow of limits can limit the generalizability of the results and make it difficult to apply them to a larger population. Additionally, setting limits may also restrict the potential for unexpected or serendipitous findings.

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