AP EAMCET · Maths · Limits
Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \(\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)=\)
- A \(0\)
- B \(\frac{8}{3}\)
- C \(\frac{64}{27}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 2^{+}}[x] = 2\) \(\lim _{x \rightarrow 2^{+}}\left[\frac{x}{3}\right] = \left[\frac{2^{+}}{3}\right] = \left[\left(\frac{2}{3}\right)^{+}\right] = 0\)…
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