MCQ
$\lim_{x \rightarrow {{2}^{ +}}} \left[ \frac{{{\left[ x \right]}^{3}}}{3}-{{\left[ \frac{x}{3} \right]}^{3}} \right]=.......$
- A$0$
- B$\frac{64}{27}$
- ✓$\frac{8}{3}$
- Dએક પણ નહીં.
અહી , $x\in (2,3)$ માટે
$[x]=2$ અને $[x]=3$
$=\lim_{x \rightarrow 2^+}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)$
$=\frac{1}{3}\lim_{x \rightarrow 2^+}[x]^3-\lim_{x \rightarrow 2^+}\left[\frac{x}{3}\right]^3$
$=\frac{1}{3}(2)^3-0=\frac{8}{3}$
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વિધાન $- 2 :9$ સ્થાનો પૈકી કોઈપણ $3$ સ્થાનો $^9C_3$ રીતે પસંદ કરી શકાય.