#### To determine

**To show:** We have to show that limx→-∞bx=0.

#### Answer

#### Explanation

**Calculation:**

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

limx→-∞bx=0.

**Conclusion:** 0

#### To determine

**To show:** We have to show that limx→∞bx=∞.

#### Answer

**Answer: ∞**

#### Explanation

**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.

Thus, we have

limx→∞bx=∞.

**Conclusion: ∞**