How to go about the proof of the limit of $\ln(x+y)$ being equal to $\ln(4\pi/3)$ as $(x,y)$ approaches $(\pi,\pi/3)$.

  • $\begingroup$ What does $\ln$ mean to you? $\endgroup$
    – user61527
    May 20, 2014 at 22:01
  • $\begingroup$ An abbreviation for natural logarithm $\endgroup$ May 20, 2014 at 22:04
  • $\begingroup$ Yes, and how have you defined the natural logarithm? $\endgroup$
    – user61527
    May 20, 2014 at 22:04

1 Answer 1


As $(x,y) \rightarrow (\pi\frac{\pi}{3})$, $x+y\rightarrow \frac{4\pi}{3}$. Now use the fact that $\ln$ is continuous. And $\lim_{a \to \frac{4\pi}{3}}\ln(a)=\ln (\frac{4\pi}{3})$.

  • $\begingroup$ I can't figure out what to do here $\endgroup$ Jun 13, 2014 at 19:55

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