求lim[x趨於無窮]{(x^3)*ln[(x+1)/(x-1)]-2x^2},答案為2/3,

求lim[x趨於無窮]{(x^3)*ln[(x+1)/(x-1)]-2x^2},答案為2/3,

lim[x趨於無窮]{(x^3)*ln[(x+1)/(x-1)]-2x^2}
=lim[x趨於無窮]{(x^2){xln[(x+1)/(x-1)]-2}
=lim[x趨於無窮]{xln[1+2/(x-1)]-2}/[x^(-2)]
=lim[x趨於無窮]{ln[1+2/(x-1)]+x[1+2/(x-1)]^(-1)[-2/(x-1)^2]}/[-2x^(-3)]
=lim[x趨於無窮]{-2x/(x-1)^2[-2x^(-3)]
=2/3