text: calculus limit problem? would you guys help me with a problem i have.  what is the limit as x goes to 0 of:  (1/x)-cot(x)  thanks in advance for the help.  if you could work it out step by step that would be awesome. lim ((1/x) - cot(x))=  lim ((1/x)- cosx/sinx)=  lim [(sinx-xcosx)/xsinx]=  this is in the form 0/0  and you can use lopital's rule   lim [(cosx-cosx+xsinx)/ (sinx+xcosx)]=  lim[(xsinx)/(sinx + xcosx)]  and this is again 0/0   =lim [(sinx+xcosx)/ (cosx+cosx-xsinx)]=  (sin0+0*cos0)/ (cos0+cos0-0*sin0)=  0/2=  0