dumbcow
  • dumbcow
lim as n->infinity [n*tan(pi/n)]
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
you can use the squeeze theorem here ^_^
nikvist
  • nikvist
\[\lim_{n\rightarrow\infty}n\cdot\tan\frac{\pi}{n}=\lim_{n\rightarrow\infty}\frac{n}{\cot\frac{\pi}{n}}= \lim_{n\rightarrow\infty}\frac{1}{-\frac{1}{\sin^2\frac{\pi}{n}}}=-\lim_{n\rightarrow\infty}\sin^2\frac{\pi}{n}=0\]
nikvist
  • nikvist
my wrong

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dumbcow
  • dumbcow
hmm interesting yeah i know its pi but can seem to show it mathematically
anonymous
  • anonymous
the answer must be zero :)
dumbcow
  • dumbcow
i seem to always get an indeterminate limit, even when using L'hopitals rule repeatedly
dumbcow
  • dumbcow
sstarica, graph function and you will see limit is not 0
nikvist
  • nikvist
\[\lim_{n\rightarrow\infty}n\cdot\tan\frac{\pi}{n}= \lim_{m\rightarrow 0}\frac{\pi}{m}\cdot\tan{m}= \pi\cdot\lim_{m\rightarrow 0}\frac{\tan{m}}{m}= \pi\cdot\lim_{m\rightarrow 0}\frac{1}{\cos^2{m}}=\pi\]
dumbcow
  • dumbcow
ahh like u substitution to avoid chain rule...thank you very much
anonymous
  • anonymous
Thank You! Why?

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