1.lim x->无穷 x*sin(2x/(x^2+1)) 2
问题描述：
1.lim x->无穷 x*sin(2x/(x^2+1)) 2
2.lim x->正无穷 ((x^2-1)/(x^2+1))^(x^2) e^-2
答
1.
lim x->无穷x*sin(2x/(x^2+1))
令x=1/t, t->0
得
lim t->0sin((2/t)/((1/t)^2+1))/t
=lim t->0sin((2t)/((1+t^2))/t
=lim t->0((2t)/((1+t^2))/t
=2
2. lim x->正无穷((x^2-1)/(x^2+1))^(x^2)
=lim x->正无穷((1+(-2)/(x^2+1))^(x^2)
=e^(limx->正无穷(-2)(x^2)/(x^2+1))
=e^(-2)