limx→∞(xsin2/x+sin2x/x)=

Question

lim x→∞(xsin2/x+sin2x/x)=

Answer 1

根据sinx/x=1(x-0)；
=lim(xsin2/x+sin2x/x)(由于x无穷,所以后面一项趋近于0)
=lim(xsin2/x)
令t=1/x,则t->0
lim(sin2t/t)
=lim2(sin2t/2t)
=2;