求limx(x趋向无穷)乘以tan1/x的过程,谢谢.

求limx(x趋向无穷)乘以tan1/x的过程,谢谢.
求limx(x趋向无穷)乘以tan1/x的过程,谢谢.

求limx(x趋向无穷)乘以tan1/x的过程,谢谢.
lim(x→∞)xtan(1/x)=lim(x→∞)[sin(1/x)/(1/x)]*cos(1/x)
=lim(1/x→0)sin(1/x)/(1/x)lim(1/x→0)cos(1/x)=1*1=1