Sunday, 23 March 2014

calculus - A simple-looking rational limit



Please help me compute:
limz02(zlog(1+z))z
I know the answer is 1 because I plugged it into Mathematica. Attempts with L'Hopital's Rule didn't work. This a step in an exercise for my self-study project. Thanks!


Answer




Using Taylor series
log(1+z)0zz22
we get



2(zlog(1+z))z0|z|z{1at0+1at0
so the limit doesn't exist.


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