AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty} \frac{[2 x-3]}{x}=\)
- A \(0\)
- B \(\infty\)
- C \(-3\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { We know, } x-1 \lt [x] \leq x \\ & \Rightarrow 2 x-4 \lt [2 x-3] \leq 2 x-3 \\ & \Rightarrow 2-\frac{4}{x} \lt \frac{[2 x-3]}{x} \leq \frac{2-3}{x} \\ & \lim _{x \rightarrow \infty}\left(2-\frac{4}{x}\right) \lt \lim _{x \rightarrow \infty} \frac{[2…
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