F4 LIMIT 一問

Since x-->-∞
so x become negative real no
For the negative index, as we know that it can become the denominator of the fraction
eg:2^(-x)=1/(2^x)

lim(x->-∞)[2^2x-1/2^2x+1]
=lim(x->+∞)[1/2^2x-1/1/2^2x+1]
as lim(x->+∞)[1/2^2x]=0
so lim(x->-∞)[2^2x-1/2^2x+1]
=0-1/0+1=-1

2011-05-12 19:04:24 補充：
多謝你既問題，
如有問題，
歡迎再次發問

2011-05-13 11:18:32 補充：
Q1)As I said before, the negative index can denominator of the fraction. So that when the limit change from-∞ to +∞ and change 2^x to 1/2^x at the same time, then the ans become the same and it can imply the next step.
ie.lim(x->-∞)[2^2x-1/2^2x+1]=lim(x->+∞)[1/2^2x-1/1/2^2x+1]

2011-05-13 11:18:39 補充：
Q2) only lim(x->-∞)2^x=0
lim(x->+∞)2^x does not exist
as x-->∞ then 2^x-->∞

lim(x->-∞) 2^2x
When x is negatively very very small, it tends to 0.

Btw, do u hv any questions in the first picture???

因為 lim (x->-∝) 2^x=0