1)lim (x→0)(3sinx+x^2cos(1/x))/(1+cosx)In(1+x)=lim (x→0)3sinx/[2ln(1+x)]=3/2
2)没看清题
3)lim (n→∞)(1/(n^2+n+1)+2/(n^2+n+1)+…+n/(n^2+n+1))=lim (n→∞)(1+n)n/2/(n^2+n+1)=1/2
4)(x^2+1)/(x+1)-ax+b=[(1-a)x^2-ax+1]/(x+1)+b
所以a=1,lim (x→∞)((x^2+1)/(x+1)-ax+b=lim (x→∞)(1-x)/(x+1)+b=-1+b=3
所以b=4