Question

Evaluate lim(1/x - 1/tanx) when x approach 0

Answer 1

\[\lim_{x \rightarrow 0}(\frac{ 1 }{ x }-\frac{ 1 }{ \tan x})\]

Answer 2

\[\lim_{x \rightarrow 0}(\frac{ \tan x -x }{ x \tan x })\]
So L'Hopital rule is applied.
where i should differentiate both numerator and denominator

Answer 3

Yah that sounds right. Since you have the form 0/0, you're allowed to apply L'Hop.

Answer 4

Hmm get's messy after that huh? Hmmm.

Answer 5

Yeah,its bcome complicated after differentiate.It bcome
\[\lim_{x \rightarrow 0}(\frac{ x ^{2}\sec ^{2}x-\tan ^{2}x }{ x ^{2}\tan ^{2}x })\]

Answer 6

I guess