L'Hopital's Rule for Solving Indeterminate Form (-∞)/∞

  • Thread starter kasse
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In summary, L'Hopital's Rule can be used on the indeterminate form (-∞)/∞ and mathematical signs such as ∞ and the integral sign can be written using [tex] tags. L'Hopital's Rule can also be applied to other indeterminate forms, not just 0/0.
  • #1
kasse
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Can one use L'Hopital's Rule on the indeterminate form (-∞)/∞ ?

And by the way, is there a way to write mathematical signs like ∞, the integral sign etc except google-ing, cutting and pasting?
 
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  • #2
I think you can. It would probably be:

[tex] -\lim_{x\rightarrow c} \frac{f(x)}{g(x)} [/tex] so that both functions approach [tex] \infty [/tex]

you write those signs in [tex] tags as follows: \infty \int
 
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  • #3
Yes, it's a french name. But that doesn't really help me a lot :tongue2:
 
  • #4
OK, thanks!
 
  • #5
I'm not sure, I think its only 0/0, as it comes from the Taylor expansion about the point that x approaches, ie.

[tex]\lim_{x\rightarrow a}\frac{f(x)}{g(x)} = \lim_{x\rightarrow a}\frac{f(a) + f'(x)(x-a) + ...}{g(a) + g'(x)(x-a) + ...} = \lim_{x\rightarrow a}\frac{f'(x)}{g'(x)}[/tex]

With f(a)=g(a)=0

Something like that anyway.
 
  • #6
No you can use L'Hopitals Rule for indeterminate forms, not just 0/0.
 

What is L'Hopital's rule for solving indeterminate form (-∞)/∞?

L'Hopital's rule is a mathematical technique used to evaluate limits involving indeterminate forms, such as when the numerator and denominator both approach infinity or zero. It states that the limit of a fraction can be found by taking the derivative of the numerator and denominator separately and then evaluating the limit again.

What is an indeterminate form?

An indeterminate form is an expression that does not have a definite value when the limit is taken. This can occur when both the numerator and denominator approach infinity, or when they both approach zero. In these cases, L'Hopital's rule can be applied to determine the limit.

How do you use L'Hopital's rule to solve (-∞)/∞?

To solve (-∞)/∞ using L'Hopital's rule, take the derivative of the numerator and denominator separately. Then, evaluate the limit again using the new expressions. If the new limit is still indeterminate, repeat the process until a finite result is obtained.

Is L'Hopital's rule the only way to solve (-∞)/∞?

No, L'Hopital's rule is not the only way to solve (-∞)/∞. Other techniques such as algebraic manipulation, substitution, and factoring may also be used depending on the specific problem.

Are there any limitations to using L'Hopital's rule for solving (-∞)/∞?

Yes, there are limitations to using L'Hopital's rule for solving (-∞)/∞. This rule can only be applied to certain types of indeterminate forms, and it may not always yield a correct or meaningful result. It is important to understand the conditions and assumptions for using L'Hopital's rule before applying it.

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