Limit of Indeterminate Form (0/0) using L'Hopital Rule

In summary, the conversation discusses a problem with finding a limit using L'Hopital's rule, resulting in an indeterminate form of 0/0. The individual asks for help and receives a hint to simplify the answer using algebra, leading to a final answer of -1.
  • #1
planauts
86
0

Homework Statement


http://puu.sh/1irk2


Homework Equations





The Attempt at a Solution


I am having trouble doing this question. I tried doing the L'Hopital but didn't work. When I subbed in 0 in the function, I got 0/0.

first time:
I got that: http://puu.sh/1iroz

It still gave me the indeterminate form (0/0). Could someone give me a hint on solving this limit, I know the answer is 0 (used wolframalpha) but I am unsure why it is.

Thanks
 
Last edited by a moderator:
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  • #2
Use L'Hopital's rulke again on the new limit.
 
  • #3
planauts said:

Homework Statement


http://puu.sh/1irk2


Homework Equations





The Attempt at a Solution


I am having trouble doing this question. I tried doing the L'Hopital but didn't work. When I subbed in 0 in the function, I got 0/0.

first time:
I got that: http://puu.sh/1iroz

It still gave me the indeterminate form (0/0). Could someone give me a hint on solving this limit, I know the answer is 0 (used wolframalpha) but I am unsure why it is.

Thanks

Use algebra to simplify your answer. I don't think the limit is zero.
 
Last edited by a moderator:
  • #4
I also did not get zero

I would not suggest using L'hospital's rule again, it can be simplified to give you a limit which is not zero I believe
 
  • #5
Nevermind, you are right. It is -1. I redid it, when I simplified it, all the x's that led to the evil division of zero disappeared.

Thanks
 

FAQ: Limit of Indeterminate Form (0/0) using L'Hopital Rule

What is L'Hopital's Rule?

L'Hopital's Rule is a mathematical technique used to evaluate limits involving indeterminate forms such as 0/0 or ∞/∞. It states that for a fraction f(x)/g(x) where f(x) and g(x) both approach 0 or ∞ as x approaches a certain value, the limit of the fraction can be found by taking the limit of the derivative of f(x) divided by the derivative of g(x).

When is L'Hopital's Rule applicable?

L'Hopital's Rule is applicable when evaluating limits of indeterminate forms, such as 0/0 or ∞/∞. It is also applicable when evaluating limits at infinity, where the numerator and denominator both approach either 0 or ∞ as x approaches infinity.

How do you use L'Hopital's Rule?

To use L'Hopital's Rule, you must first determine if the limit is in an indeterminate form. If it is, take the derivative of both the numerator and the denominator. Then, evaluate the limit of the resulting fraction. If the resulting limit is still in an indeterminate form, repeat the process until a definitive answer is obtained.

What are the common mistakes when using L'Hopital's Rule?

One common mistake when using L'Hopital's Rule is to forget to check if the limit is in an indeterminate form before applying the rule. Another mistake is to take the derivative of the denominator more than once, as this can lead to incorrect results. It is also important to remember to evaluate the limit of the resulting fraction after each application of the rule.

Are there any limitations to L'Hopital's Rule?

Yes, there are certain limitations to L'Hopital's Rule. It can only be applied to limits involving indeterminate forms, and it is not applicable to limits that approach infinity at different rates. Additionally, it cannot be used to evaluate limits that involve trigonometric functions, logarithmic functions, or exponential functions, as these functions have specific limit properties that must be used instead.

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