Does $limlimits_{xto3} (4 - x)^{tan (frac {pi x} {2})}$ converge?

I would like to evaluate the following limit: $$limlimits_{xto3} (4 – x)^{tan (frac {pi x} {2})} .$$

---

My working

begin{align}
limlimits_{xto3} (4 – x)^{tan (frac {pi x} {2})} & =
expleft(limlimits_{xto3} ln left( (4 – x)^{tan (frac {pi x} {2})} right)right)
\[5 mm] & =
expleft(limlimits_{xto3} frac {ln (4 – x)} {cot frac {pi x} {2}}right)
\[5 mm] & =
expleft(limlimits_{xto3} left[left(frac {-1} {4 – x}right) div left(-csc^2 (frac {pi x} {2})right)right]right)
\[5 mm] & =
expleft(limlimits_{xto3} frac {sin^2 (frac {pi x} {2})} {4 – x}right)
\[5 mm] & =
e
end{align}

---

However, I get conflicting results when I try to check my answer.

Firstly, a plot of $y = (4 – x)^{tan (frac {pi x} {2})}$ using a graphing software like Desmos shows that as $x rightarrow 3$, $y$ converges to some value slightly less than $2$ (not sure what the value is, but it definitely does not look like $2.71828…$).

Secondly, I tried to evaluate the limit directly using software such as Symbolab and it tells me that the limit diverges.

Is my working correct? If not, where did I go wrong? Also, if my answer is indeed correct, why is it that software such as Symbolab cannot evaluate this limit? Is there a limitation to such softwares (no pun intended)? And why then, does the graph that I plotted not converge to $e$?

Any help/intuition/explanation will be greatly appreciated 🙂

---

Edit

So following my accepted answer below, it seems that Desmos was correct and I was careless. However, it seems there still is no explanation as to why Symbolab cannot evaluate this limit. If anyone is familiar with the technicalities of the software and perhaps knows why this is the case, do drop a comment/answer too 🙂