Question

$\underset{x\to \infty }{\lim }\frac{\log [x]}{x}$, where [.] denotes greatest integral function, is

• A. 0
• B. 1
• C. -1
• D. none of these

Answer 1

Answer: (A)

$\underset{x\to \infty }{\lim }\frac{\log [x]}{x}=\underset{x\to \infty }{\lim }\frac{\log x}{x}$
$(\because$ when $x\to \infty ,[x]\approx x$ )
$=\underset{x\to \infty }{\lim }\frac{\frac{1}{x}}{1}=0$
(Applying L' Hospital's rule)