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प्रश्न
Find \[\lim_{x \to 5/2} \left[ x \right] .\]
उत्तर
\[\text{ LHL }: \]
\[ \lim_{x \to \frac{5}{2}^-} \left[ x \right]\]
\[\text{ Let } x = \frac{5}{2} - \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ \frac{5}{2} - h \right]\]
\[ = 2\]
\[\text{ RHL }: \]
\[ \lim_{x \to \frac{5}{2}^+} \left[ x \right]\]
\[\text{ Let } x = \frac{5}{2} + \text{ h, where h } \to 0 . \]
\[ \lim_{h \to 0} \left[ \frac{5}{2} + h \right]\]
\[ = 2\]
We know:
\[\lim_{x \to \frac{5}{2}} \left[ x \right] = \lim_{x \to \frac{5}{2}^-} \left[ x \right] = \lim_{x \to \frac{5}{2}^+} \left[ x \right]\]
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