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Evaluate underset(x to oo) lim ([x])/(2...

Evaluate ` underset(x to oo) lim ([x])/(2x)`

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To evaluate the limit \( \lim_{x \to \infty} \frac{[x]}{2x} \), where \([x]\) denotes the greatest integer function (also known as the floor function), we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Greatest Integer Function**: The greatest integer function \([x]\) gives the largest integer less than or equal to \(x\). Therefore, we can express it as: \[ [x] \leq x < [x] + 1 ...
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