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

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SUMMARY

The limit of the function f(x) = (-1 + e^x) / x as x approaches 0 can be effectively solved using L'Hôpital's Rule or by expanding e^x into its Taylor series. The Taylor series expansion of e^x around x = 0 provides a straightforward method to evaluate the limit. Both techniques lead to the conclusion that the limit equals 1.

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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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Try l'hospital's rule.

Or expand e^x into its Taylor series.
 
Oh man of course l'hospital's rule! Thanks for refreshing my memory!
 

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