text: lim ((1/x) - cot(x))=\n\nlim ((1/x)- cosx/sinx)=\n\nlim [(sinx-xcosx)/xsinx]=\n\nthis is in the form 0/0 \nand you can use Lopital's Rule\n\n\nlim [(cosx-cosx+xsinx)/\n(sinx+xcosx)]=\n\nlim[(xsinx)/(sinx + xcosx)] \nand this is again 0/0\n\n\n=lim [(sinx+xcosx)/\n(cosx+cosx-xsinx)]=\n\n(sin0+0*cos0)/\n(cos0+cos0-0*sin0)=\n\n0/2=\n\n0