Question

微积分 26题？

应该怎么写啊
求过程

Answer 1

因为对∀x=c，有lim(h->0) sin(c+h)
=lim(h->0) sinc*cosh+cosc*sinh
=sinc*1+cosc*0
=sinc
所以f(x)=sinx在任意点x=c处连续
同理，因为对∀x=c，有lim(h->0) cos(c+h)
=lim(h->0) cosc*cosh-sinc*sinh
=cosc*1-sinc*0
=cosc
所以g(x)=cosx在任意点x=c处连续

追问

26题

Answer 2

(1)lim(x->∞) (1 +1/x^3)^x =e^0 =1
(2)lim(x->∞) (1 -1/x^3)^x =e^0 =1
(3)lim(x->∞) (1 +1/x)^(x^3) ->+∞
(4)lim(x->∞) (1 -1/x)^(x^3) ->0

追问

那个e是怎么出来的啊

追答

lim(x->∞) (1 +1/x^3)^x
=lim(x->∞) e^[x.ln(1 +1/x^3) ]
=lim(x->∞) e^[x.(1/x^3) ]
=lim(x->∞) e^(1/x^2)
=e^0
=1