Calculus Help Please Urgent!!!
posted by Selda on .
find the limit algebraically. Use L'Hospital's Rule where appropriate. If there is a moare elementary method, consider using it. If L'Hospital's Rule doesn't apply, explain why
lim > 0 (cot(x)(1/x))
show work please!!!

lim > 0 (cot(x)(1/x)) , x> 0
= sec^2 x + 1/x^2 by L'Hospital's Rule
but that is just as bad
try experimentally ... using a Calculator
let x = .0001
I get .0000333
let x = .000001
my calculator says 0
http://www.wolframalpha.com/input/?i=limit+cot%28x%29++1%2Fx+%2C+x+%3D+0
the red dot shows the value of the limit 
Hmmm. we all know that
tan x > x as x>0
so, cot x > 1/x as x>0
so the limit ought to be zero.