lim(x趋向无穷)((3-2x)/(2-2x))^x

问题描述:

lim(x趋向无穷)((3-2x)/(2-2x))^x

(3-2x)/(2-2x)=1+1/(2-2x)
令t=1/(2-2x),则x=1-(1/2t)则x→无穷时,t→0
lim(x趋向无穷)((3-2x)/(2-2x))^x
=lim(t→0)(1+t)^[1-(1/2t)]
=lim(t→0)(1+t)/√[(1+t)^1/t]
=1/√e
=e^-1/2