x是趋于无穷的吧
lim(x趋于无穷)(1+2/x)^3x
=lim(x趋于无穷)(1+2/x)^(x/2*6)
=lim(x趋于无穷)[(1+2/x)^(x/2)] ^6
显然由重要极限知道,
lim(x趋于无穷) (1+2/x)^(x/2)=e,
所以
原极限
=lim(x趋于无穷)[(1+2/x)^(x/2)] ^6
=e^6