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The function is f(x)= (x^n - x^{-n} ) / ( x - x^{-1} ) Can we...

The function is

f(x)= (x^n - x^{-n} ) / ( x - x^{-1} )

Can we use L'Hopital rule if n is a complex eigenvalue ?
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Answer #1

Yes. it can be used. L' Hospital rule works locally. That means you check limits in a neighborhood of the point. For details you can check https://math.stackexchange.com/questions/602650/is-lhopitals-rule-applicable-to-complex-functions.

Here is the solution anyway.

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