Question

can somebody help me ? how to evaluate lim x approach to 0 .. (x-π)cot x ?

Answer 1

\[\lim_{x \rightarrow 0}(x-\pi )(\frac{ 1 }{ \tan(x) })\] plug in 0
\[\lim_{x \rightarrow 0}(0-\pi)(\frac{ 1 }{ \tan(0) })\]
\[\lim_{x \rightarrow 0}\frac{ 1 }{ 0 }=?\]

Answer 2

*edit typo\[\lim_{x \rightarrow 0}\frac{ -\pi }{ 0 }\]

Answer 3

can i use the l'hospital's rule for this question ?

Answer 4

Actually I dont think you can as when you plug in x=0 it does not result in 0/0 or infinity/infinity

Answer 5

\[\lim_{x \rightarrow 0}(x-\pi) ~ \cot(x) \]

\[= \lim_{x \rightarrow 0}(x-\pi)~~ \dfrac{ 1 }{ \tan(x) }\]

\[= - \pi \lim\limits_{x \to 0} \dfrac{1}{ \tan(x) } \]


no idea where it goes from here.

Answer 6

;-)

Answer 7

thanks