Ok, so I'm suppose to be able to remove the singularity to find the residue of the function(adsbygoogle = window.adsbygoogle || []).push({});

[tex](z)cos{\frac{1}{z}[/tex]

I tried to see how "bad" the singularity was by taking the limit, but I can't figure out if

[tex]

\lim_{ z \to 0 } (z)cos{\frac{1}{z}

[/tex]

goes to 0 or if it is not bounded. If it goes to zero I should be able to remove the singularity. Since I couldn't figure that out I used the Taylor Series of cos(z) to expand the function and I got a Laurent Series.

[tex](z)cos{\frac{1}{z} = \sum_{n=0}^\infty \frac{(-1)^{(n)}}{(2n)!}z^{(-2n+1)} [/tex]

This is where I'm stuck. I don't see how I can possibly remove the singularity or if its even removable. Any ideas?

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# Complex Analysis - Removing A Singularity

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