设y=(5x+3)/(3x^2+5)
limy=0
limsin(4/x)=0
limsin(4/x)/y=limcos(4/x)(-4/x^2)/y'
y'=-(15x^2+18x-25)/(3x^2+5)^2
limsin(4/x)/y=limcos(4/x)(-4/x^2)/y'=limcos(4/x)/y2
其中y2=x^2*(15x^2+18x-25)/(3x^2+5)^2
limcos(4/x)=1
limy2=15/9=5/3
故
lim(3x^2+5)/(5x+3)*sin4/x=1/(5/3)=3/5