Let's evaluate the limit of $\ln \left(\sin \left(x\right)\right)$ when $x\to \pi$

ⓘ The function sin is continuous, its limit is its value at the limit of its argument

The limit of $\sin \left(x\right)$ is $\sin \left(\pi \right)$ when $x\to \pi$

⇥Let's evaluate: $\sin \left(\pi \right)$

⇥ⓘ The sine is the y-coordinate (vertical axis) of the point reached on the unit circle after a rotation of $\pi$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\sin \left(\pi \right)$ = $0$

⇥ $0$

So the limit of $\ln \left(\sin \left(x\right)\right)$ does not exist when $x\to \pi$

▶Limit:   $\mathrm{undefined}$