Lim x -> 0: Solve f(x) = (-1+e^x) / x

  • Thread starter DemoniWaari
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In summary, the conversation revolved around finding the limit of a function using different methods, such as Taylor's series and l'Hopital's rule. The person seeking help was struggling to solve it on their own and appreciated the reminder of l'Hopital's rule.
  • #1
DemoniWaari
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Hey there, I was trying to check my calculations of one laplace tranformation and I needed to know a limit: f(x) = (-1+e^x) / x as x -> 0. And I can't seem to find the answer for this even though I try and try. So little help?

Oh I was just thinking that can you use taylor's series for this? Wolfram found some interesting series at x = 0 and I was thinking that it might give me the answer too, though I can't solve it either so help with that is greatly appreciated...
 
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  • #2
Try l'Hopitals rule.

Or expand [itex]e^x[/itex] into its Taylor series.
 
  • #3
Oh man of course l'Hopitals rule! Thanks for refreshing my memory!
 

1. What is the limit of f(x) as x approaches 0?

The limit of f(x) as x approaches 0 is undefined.

2. How do you solve for f(x) when x approaches 0?

To solve for f(x) when x approaches 0, we can use L'Hôpital's rule. This rule states that if the limit of f(x) as x approaches a is indeterminate (such as 0/0), we can take the derivative of both the numerator and denominator and then evaluate the limit again.

3. What is the value of f(x) at x = 0?

The value of f(x) at x = 0 is also undefined.

4. Can the limit of f(x) as x approaches 0 be solved without using L'Hôpital's rule?

No, the limit of f(x) as x approaches 0 cannot be solved without using L'Hôpital's rule or a similar method that involves taking the derivative of the function.

5. How does the function behave as x approaches 0 from the left and right?

As x approaches 0 from the left, the function approaches negative infinity. As x approaches 0 from the right, the function approaches positive infinity. This is because the numerator, (-1+e^x), approaches -1 from the left and 1 from the right, while the denominator, x, approaches 0 from both sides.

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