Can the equation be simplified in the third step if it's indeterminate?

  • Thread starter MathewsMD
  • Start date
  • Tags
    Simplify
In summary: In this case, l'Hospital's rule is used to find the limit. So, in summary, the equation cannot be simplified in the third step where it specifies that the equation is indeterminate because ln1 = 0, resulting in the indeterminate form 0/0. The solution uses l'Hospital's rule to find the limit, as dividing by 0 is undefined.
  • #1
MathewsMD
433
7
pbYtOEe.png


Why can't the equation be simplified in the third step where it specifies that the equation is indeterminate? You could essentially have ln1/(ln1+1-1) if you substitute values in here. This then simplifies to just ln1/ln1 and then they would cancel to equal 1. Yet, the solution uses l'Hospital's rule again but it seems simplifiable here at this intermediate step. Any clarification is greatly appreciated!
 
Physics news on Phys.org
  • #2
MathewsMD said:
pbYtOEe.png


Why can't the equation be simplified in the third step where it specifies that the equation is indeterminate? You could essentially have ln1/(ln1+1-1) if you substitute values in here. This then simplifies to just ln1/ln1 and then they would cancel to equal 1.
No, because ln1 = 0. The fraction would simplify to 0/(0 + 1 - 1), so you're at the indeterminate form [0/0].
MathewsMD said:
Yet, the solution uses l'Hospital's rule again but it seems simplifiable here at this intermediate step. Any clarification is greatly appreciated!
 
  • #3
Mark44 said:
No, because ln1 = 0. The fraction would simplify to 0/(0 + 1 - 1), so you're at the indeterminate form [0/0].

But is not the same as 5/(5+1-1) = 5/5 = 1 or x/(x+1-1) = x/x = 1, where the numerator and denominator become the same? Are we not allowed to do this since these are limits and not exactly these values or is there another reason?
 
  • #4
No, it's not the same. You can say ##x/x=1## only when ##x\ne 0##, otherwise, it's undefined.

If a limit results in 0/0, it's indeterminate, and you need to do some work to figure out if the limit exists.
 

Related to Can the equation be simplified in the third step if it's indeterminate?

1. Why is it important to simplify earlier in the scientific process?

Simplifying earlier in the scientific process can save time and resources by reducing the complexity of the problem. It also allows for a clearer understanding of the variables involved and can lead to more accurate and efficient results.

2. Can simplifying too early in the process lead to biased or inaccurate results?

Yes, simplifying too early in the process can potentially lead to biased or inaccurate results. It is important to carefully consider which variables can be simplified without significantly impacting the overall outcome.

3. How do scientists determine when to simplify in their research?

Scientists determine when to simplify in their research by carefully analyzing the problem and identifying which variables are essential to the experiment. They also take into account the potential impact of simplifying certain variables on the overall results.

4. Are there any drawbacks to simplifying earlier in the scientific process?

One potential drawback to simplifying earlier in the scientific process is that it may limit the scope and applicability of the results. Additionally, simplifying too much can oversimplify the problem and lead to less meaningful or applicable findings.

5. How does simplifying earlier in the process benefit the scientific community?

Simplifying earlier in the process can benefit the scientific community by improving the efficiency and accuracy of research. It can also make findings more accessible and applicable to a wider audience, leading to potential advancements in various fields.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
147
  • Calculus and Beyond Homework Help
Replies
2
Views
790
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
852
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • General Math
Replies
23
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
687
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top