lim[x-->+∞][(-1/2)e^(-2x)x-1/4e^(-2x)+1/4]
=lim[x-->+∞](-1/2)e^(-2x)x+1/4
=1/4+lim[x-->+∞](-1/2)x/e^(2x)
=1/4+lim[x-->+∞](-1/2)/[2e^(2x)]
=1/4