Why does the function $\frac{1}{x^{2222}}$ seem to have *two* asymptotes at around $\pm0.744$?

Question

When screwing around with the Dirac-delta function in Desmos i noticed that when i multiply it by a really low-degree rational function

$$f(x)=\frac{1}{x^i}$$

, the resulting function has the domain

$$D\supset\mathbb{R}\setminus[-\varepsilon,\varepsilon]$$ where $\varepsilon$ is a positive real number.

Now of course this has to be false because $f(x)$ only has roots at $0$, so having only one asymptote.

Is this a computational/floating point error?I checked it and Geogebra has the same kind of error.

Why does the function $\frac{1}{x^{2222}}$ seem to have two asymptotes at around $\pm0.744$?

Answer 1

You can see the answer in any standard programming language. Here is what we see in Python, which uses 64-bit floats (sys.getsizeof(1.0) returns 24 == 16 (Python bloat) + 8 (bytes to represent float)):

In[1]: 1/(.73 ** 2222)
Out[1]: 4.972843735306971e+303
In[2]: 1/(.72 ** 2222)
Out[2]: inf

Somewhere between .73 and .72 is exactly the point at which $\frac{1}{x^{2222}}$ exceeds the largest representable floating point number, triggering it to be "inf" (infinity).