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  • <img alt="\mathrm{\lim _{x \rightarrow \infty} \frac{\ln [x]}{x}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B%5Cln%20

\mathrm{\lim _{x \rightarrow \infty} \frac{\ln [x]}{x}}

Option: 1

equal to 1
 


Option: 2

equal to 0
 


Option: 3

equal to -1
 


Option: 4

Does not exist


Answers (1)

best_answer

\mathrm{\begin{array}{ll} & x-1 \leq[x] \leq x \\\\ \Rightarrow \quad & \frac{\ln (x-1)}{x} \leq \frac{\ln [x]}{x} \leq \frac{\ln x}{x} \\\\ \Rightarrow \quad & \lim _{x \rightarrow \infty} \frac{\ln [x]}{x}=0 \end{array}}

Posted by

Irshad Anwar

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