高数lim(x→∞)[(3+x)/(6+x)]^[(x
lim(x→∞)[(3+x)/(6+x)]^[(x-1)/2]
原式=lim(x→∞)[(6+x-3)/(6+x)]^[(x-1)/2] =lim(x→∞){[1-(3/6+x)]^[(6+x)/(-3)]}^{[-3/(6+x)]*[(x-1)/2]} =e^lim(x→∞)[-3/(6+x)]*[(x-1)/2] =e^lim(x→∞)[(-3/2)*(x-1)/(6+x)] =e^(-3/2).