Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

$\lim\limits_{x \rightarrow \infty} \frac{\ln [x]}{x}=$

Options:

1

0

-1

does not exist

Correct Answer:

0

Explanation:

x - 1 ≤ [x]  ≤ x

$\Rightarrow \frac{\ln (x-1)}{x} \leq \frac{\ln [x]}{x} \leq \frac{\ln x \mid}{x} \Rightarrow \lim\limits_{x \rightarrow \infty} \frac{\ln [x]}{x}=0$

Hence (2) is the correct answer.