## dumbcow 5 years ago lim as n->infinity [n*tan(pi/n)]

1. anonymous

you can use the squeeze theorem here ^_^

2. nikvist

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

3. nikvist

my wrong

4. dumbcow

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

5. anonymous

the answer must be zero :)

6. dumbcow

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

7. dumbcow

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

8. nikvist

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

9. dumbcow

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

10. anonymous

Thank You! Why?