find limit x->pi [(x-pi).cotx].

I am stuck at x-pi/tanx

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- April 23rd 2013, 11:56 PMkastamonulimit
find limit x->pi [(x-pi).cotx].

I am stuck at x-pi/tanx - April 23rd 2013, 11:58 PMMarkFLRe: limit
Have you tried L'Hôpital's rule?

- April 24th 2013, 12:02 AMkastamonuRe: limit
no. But I found the answer.

- April 24th 2013, 12:03 AMkastamonuRe: limit
tanx=tan(x-pi) and this makes 1.

- April 24th 2013, 02:21 AMProve ItRe: limit
- April 25th 2013, 06:35 AMkastamonuRe: limit
Many Thanks. I found it by using tanx/x=1

- April 25th 2013, 06:42 AMkastamonuRe: limit
`tan (a - b)` = `(tan a - tan b)/(1 + tan a*tan b)`

`tan (x - pi )` = `(tan x - tan pi)/(1 + tan x*tan pi)`

tan pi = sin pi/cos pi = 0/-1 = 0`

`tan (x - pi) = (tan x - 0)/(1 + tan x*0)`

`tan(x - pi) = tan x`