To show: We have to show that limx→-∞bx=0.
To show limx→-∞bx=0, we have to find N such that for any ϵ>0
bx-0<ϵ when x<N
We know that bx<ϵ⇔x<logbϵ.
Let x=logbϵ. So x<N which implies bx-0<ϵ.
Thus, we have
To show: We have to show that limx→∞bx=∞.
Calculation: To show limx→∞bx=∞, we have to find N such that for any K>0
bx-0>K when x>N
We know that bx>K⇔x>logbK.
Let x=logbK. So x>N which implies bx-0>K.