I asked Wolfram Alpha to solve
$$ \lim_{x\to 0}\frac{\delta(x)}{x} $$
And the answer is $0$, without further information. Shouldn't it be $\infty$?
2026-04-06 20:42:32.1775508152
A distributional limit involving delta funciton
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If $\delta(x)=0$ for $x \not=0$ then this could lead to Wolfram Alpha saying $$\lim_{x\to 0}\frac{\delta(x)}{x} = \lim_{x\to 0}\frac{0}{x} = \lim_{x\to 0}0 = 0$$