Question

帮忙求极限

Answer 1

原式=lim(x->0) (1/x-cosx/sinx)
=lim(x->0) (sinx-xcosx)/xsinx
=lim(x->0) (sinx-xcosx)/x^2
=lim(x->0) (cosx-cosx+xsinx)/2x
=lim(x->0) sinx/2
=0

Answer 2

lim(x->0) (1/x - cotx )
=lim(x->0) (tanx -x)/(xtanx)
=lim(x->0) (tanx -x)/x^2 (0/0)
=lim(x->0) [(secx)^2 -1]/(2x) (0/0)
=lim(x->0) [2(secx)^2.tanx]/2
=0