求教4道高数题,据说很简单,但是我大一学的全忘记了

1、lime^(n+1)ln(1+2/(2n+1))
=lim e^(n+1)(2/(2n+1))
=e^lim(1+1/(2n+1))
=e
2、lim (x 1-)x+1=2
ax+b=a+b=2
lim(x 2-)3x=6
ax+b=2a+b=6
联立解得a=4 ,b=-2
3、e^xdy+e^xydx+dy/y=0
化简得dy=(-y^2e^x)/(ye^x+1)dx
y'=(-y^2e^x)/(ye^x+1)
4、令3x=t
(1/3)∫1/sint^2dt
=(-1/3)cott+C
=(-1/3)cot3x+C