1、求极限lim(1/x - cotx) ,x趋近于0

(1)
lim(x->0) (1/x -cotx)
=lim(x->0) (1/x -1/tanx)
=lim(x->0) (tanx-x)/(xtanx) (0/0)
=lim(x->0) ( (secx)^2 -1 )/ ( x(secx)^2 + tanx )
=lim(x->0) (tanx)^2/ ( x(secx)^2 + tanx )
=lim(x->0) x / ( (secx)^2 + 1 ) ( x->0 ,tanx x)
=0
(2)
f(x) =e^(2x).(1-x) - (1+x)
f'(x) = e^(2x) .(1-2x) - 1
f'(x)