Evaluating a Limit with L'Hospital's Rule

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In summary, the conversation discusses the application of L'Hospital's rule to evaluate the limit of a function involving logarithms. The individual asking for help has already attempted to solve the problem and has used the LaTeX syntax to show their work. They are requesting help with the specific steps of the solution where they may be stuck.
  • #1
Ali Muzamil
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Homework Statement
Evaluate ##\lim_{a \rightarrow b} \frac{a^b-b^a}{a^a-b^b}##

The attempt at a solution

I applied L'Hospital's rule and to differentiate it, I took the help of logs.
 
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  • #3
Greg Bernhardt said:
Please show work and use ## for latex
## ?
 
  • #5
Greg Bernhardt said:
Put your code between two sets of ##
What does ## mean?
 
  • #6
Ali Muzamil said:
What does ## mean?
It means start code and end code. See I added them to your first post.
 
  • #7
Ali Muzamil said:
The attempt at a solution
I applied L'Hospital's rule and to differentiate it, I took the help of logs.
Please show your work then. Where did you get stuck?
 

1. What is L'Hospital's Rule?

L'Hospital's Rule is a mathematical rule that is used to evaluate the limit of a function that is in an indeterminate form (such as 0/0 or ∞/∞). It states that if the limit of the ratio of two functions is in an indeterminate form, then the limit of the ratio of their derivatives will be the same as the original limit.

2. When should L'Hospital's Rule be used?

L'Hospital's Rule should only be used when the limit of a function is in an indeterminate form, and all other methods of evaluating the limit have failed. It is also important to note that the rule only applies to certain types of indeterminate forms, such as 0/0 and ∞/∞.

3. Can L'Hospital's Rule be used for all types of limits?

No, L'Hospital's Rule can only be used for certain types of limits, specifically those that are in an indeterminate form. It cannot be used for limits that are not in an indeterminate form, such as limits that approach a finite number.

4. Are there any limitations to using L'Hospital's Rule?

Yes, there are a few limitations to using L'Hospital's Rule. First, the rule only applies to certain types of indeterminate forms. Second, both the numerator and denominator of the original limit must be differentiable at the point of evaluation. Lastly, the limit must exist for L'Hospital's Rule to be used.

5. Can L'Hospital's Rule be used for multivariable functions?

No, L'Hospital's Rule can only be used for single-variable functions. It cannot be applied to functions with more than one variable.

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