If $[t]$ represents the greatest integer $\leq t$ then the value of $\lim_{x\to 3} \frac{11-[2-x]}{[x+10]}$ is
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When evaluating limits involving the greatest integer function $[x]$, always check the left-hand and right-hand limits separately. The value of $[f(x)]$ can change depending on which side you approach the limit point from.