Asked by help pls
lim [cotx - (1/x)]
x-->0
x-->0
Answers
Answered by
Steve
cotx - 1/x = (x-tanx)/(x tanx)
now apply L'Hospital's Rule, so the limit is also
(1-sec^2 x)/(tanx - xsec^2 x)
and again
-2sec^2 x tanx / (sec^2 x - 2sec^2 x tanx)
= -2sec^2x tanx / (sec^2x(1-2tanx))
= 0/1
so the limit is 0
now apply L'Hospital's Rule, so the limit is also
(1-sec^2 x)/(tanx - xsec^2 x)
and again
-2sec^2 x tanx / (sec^2 x - 2sec^2 x tanx)
= -2sec^2x tanx / (sec^2x(1-2tanx))
= 0/1
so the limit is 0
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.