设 y=[sin(2/x)+1]^2x
设 t=1/x
x->∞时 t->0
lny=2xln(sin(2/x)+1)=2ln(sin(2t)+1)/t
lim lny=2lim[cos(2t)*2]/[(sin(2t)+1)]=2*2/1=4
所以
lim[sin(2/x)+1]^2x=e^4