limX*lnX/(X*X+2)X趋向正无穷

limX*lnX/(X*X+2)X趋向正无穷
limX*lnX/(X*X+2)X趋向正无穷

limX*lnX/(X*X+2)X趋向正无穷
利用洛必达法则,
lim (X*lnX)/(X*X+2)
=lim lnX/(X+2/X)
=lim (1/X)/(1-2/X²)
=0/(1-0) = 0

=lim_{x趋于正无穷}ln{[(x+1)/x]^x} =lim_{x趋于正无穷}ln[(1+1/x)^x] =ln(e) =1 limx[ln(x+1)-lnx]=limx[ln((x+1)/x)