Why does $x^{-1/\ln x}$ at x = 0 equal to 1?

Question

According to Desmos $x^{-1/\ln x}$ equals 1 when $x$ is 0. I don't understand why this function equals 1 when $x$ = 0. I would think the point would not exist since $\ln 0$ does not exist. What am I missing?

Answer 1

You have to understand that computers represent numbers to a limited precision.

For exemple $0.000000000000001$ might get stored as $0$.

And since we have $$\forall x\in \mathbb{R}, x^0 = 1$$

The computer just assume it is the right value.

As a rule of thumb, use computer graphs to give you an idea of the behavior of a function, but don't be surprise if you sometimes get exotic values at points that should be undefined.