速求高数解答,lim(1-x分之3)x+2次方,x趋向无穷大,求极限.

=lim(1-3/x)^[(-x/3)*(-3(x+2)/x)]=e^(-3)(e^3的倒数)

表述不清

过程如下：
lim[x→∞](1-3/x)^(x+2)
=lim[x→∞](1-3/x)^[-3(-x/3)+2]
=lim[x→∞](1-3/x)^[-3(-x/3)]*(1-3/x)^2
=e^(-3)

这是1^∞型极限，使用重要极限lim(x→∞) [1+(1/x)]^x=e
lim(x→∞) [1-(3/x)]^(x+2)
=lim(x→∞) [1+(-3/x)]^[(-x/3)(-3/x)(x+2)]
=e^ [lim(x→∞)(-3/x)(x+2)]
=e^(-3)
=1/e³

lim[x→∞](1-3/x)^(x+2)
=lim[x→∞](1-3/x)^[-3(-x/3)+2]
=lim[x→∞](1-3/x)^[-3(-x/3)]*(1-3/x)^2
=e^(-3)