Saturday, June 23, 2018

calculus - Evaluate limxrightarrow0fracsinxx+tanx without L'Hopital




I need help finding the the following limit:



limx0sinxx+tanx



I tried to simplify to:



limx0sinxcosxxcosx+sinx



but I don't know where to go from there. I think, at some point, you have to use the fact that limx0sinxx=1. Any help would be appreciated.




Thanks!


Answer



sinxx+tanx=1xsinx+tanxsinx1/2


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