Question

郑州大学远程教育高等数学第一次网上作业

Answer 1

1. f(3)=4/8=1/2 f((x+1)/(x+5))=((x+1)/(x+5)+1)/((x+1)/(x+5)+5)=(x+1+x+5)/(x+1+5x+25)
=(2x+6)/(6x+26)=(x+3)/(3x+13)
2. 原式=lim[x→∞](sinx/x)/[sinx/(xcosx)]=1
3.原式=lim[x→∞](1-2/x)^x/(1-3/x)^x=e^(-2)/e^(-3)=e
4.f(4)=(1-2)/(1+2)=-1/3
5.原式=lim[x→1](xlnx-x+1)/[(x-1)lnx]=lim[x→1](lnx+1-1)/(lnx+1-1/x)
=lim[x→1]xlnx/(xlnx+x-1)=lim[x→1](lnx+1)/(lnx+1+1)=1/2