Question

lim as n->infinity [n*tan(pi/n)]

Answer 1

you can use the squeeze theorem here ^_^

Answer 2

\[\lim_{n\rightarrow\infty}n\cdot\tan\frac{\pi}{n}=\lim_{n\rightarrow\infty}\frac{n}{\cot\frac{\pi}{n}}=
\lim_{n\rightarrow\infty}\frac{1}{-\frac{1}{\sin^2\frac{\pi}{n}}}=-\lim_{n\rightarrow\infty}\sin^2\frac{\pi}{n}=0\]

Answer 3

my wrong

Answer 4

hmm interesting yeah i know its pi but can seem to show it mathematically

Answer 5

the answer must be zero :)

Answer 6

i seem to always get an indeterminate limit, even when using L'hopitals rule repeatedly

Answer 7

sstarica, graph function and you will see limit is not 0

Answer 8

\[\lim_{n\rightarrow\infty}n\cdot\tan\frac{\pi}{n}=
\lim_{m\rightarrow 0}\frac{\pi}{m}\cdot\tan{m}=
\pi\cdot\lim_{m\rightarrow 0}\frac{\tan{m}}{m}=
\pi\cdot\lim_{m\rightarrow 0}\frac{1}{\cos^2{m}}=\pi\]

Answer 9

ahh like u substitution to avoid chain rule...thank you very much

Answer 10

Thank You! Why?