The value of $\lim_{x\rightarrow 2^{+}}\frac{[x]-2}{x-2}$ is
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Logic Tip: Do not confuse exactly zero divided by a tiny number with the indeterminate form $0/0$. Here, the numerator is absolute $0$ *before* the limit operation is fully executed, making the entire fraction exactly $0$ at every point arbitrarily close to 2.