To determine

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

Answer

The limit is -∞.

Explanation

Calculation:

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

As x→0+, t=sin⁡x→ 0+, so

limx→0+⁡ln⁡(sin⁡x)=limt→0+⁡ln⁡t

Since limt→0+⁡ln⁡t=-∞, therefore limx→0+⁡ln⁡(sin⁡x)=-∞.

Conclusion:

The limit is -∞.