To determine

To find: Find the limit limx→0⁡ln⁡(cos⁡x)

Answer

The limit is 0.

Explanation

Calculation:

We have to find the limit limx→0⁡ln⁡(cos⁡x). Let t=cos⁡x

As x→0, t=cos⁡x→ 1, so

limx→0⁡ln⁡(cos⁡x)=limt→1⁡ln⁡t

Since limt→1⁡ln⁡t=0, therefore limx→0⁡ln⁡(cos⁡x)=0.

Conclusion:

The limit is 0.