Using L'hopital's rule in exponential function

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SUMMARY

The discussion centers on applying L'Hôpital's rule to evaluate the limit of the function \(\lim_{z\to -ia}\frac{e^{-A/(z+ ia)}}{(z+ia)^2}\). Participants noted that repeated differentiation results in an indeterminate form of 0/0. A solution was proposed to express the exponential function as a Laurent series around the point -ia, revealing that the limit does not exist due to a pole of order 2 at that point.

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Elsasw
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Is that any way to find a finite value which is not equal to zero using L'hopital's rule in

limit(z=-ia)
exp[-A/(z+ia)]/(z+ia)^2

i kept getting 0/0 after differentiation

Thank you
 
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So your problem is
[tex]\lim_{z\to -ia}\frac{e^{-A/(z+ ia)}}{(z+ia)^2}[/tex]
?
Instead, write the exponential as a Laurent series around -ia. It should be clear that you will have a "1" as the constant term and so the limit will not exist. This function has a pole of order 2 at z= -ia.
 
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Thank you very much HallsofIvy...i got what u meant..
 

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