Question

limxsin(2x/x²+1)x趋于无穷求极限的详解

Answer 1

简单计算一下即可，答案如图所示

Answer 2

令a=1/x
则a趋于0
x/(x²+1)=1/(a+1/a)
显然a+1/a趋于无穷
所以1/(a+1/a)趋于0
所以sin[2/(a+1/a)]~2/(a+1/a)

所以原式=lim(a→0)[2/(a+1/a)]/a
=lim(a→0)[2/(a²+1)]
=2