求lim(x->+∞)((x+a)/x)^(bx+c)(a≠0)的值
问题描述:
求lim(x->+∞)((x+a)/x)^(bx+c)(a≠0)的值
答
lim(x->+∞)((x+a)/x)^(bx+c)
=lim(x->+∞)((1+(a/x))^(x/a)*(a/x)(bx+c)
=lim(x->+∞)e^(a/x)(bx+c)
=lim(x->+∞)e^(ab+ac/x)
=e^ab