A) 0
B) 1
C) \[-1\]
D) non-existent
Correct Answer: A
Solution :
\[L=\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}\] |
\[\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}\le L\le \underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,x}{x}\] |
\[\underset{x\,\to \,\infty }{\mathop{Limit}}\,\left( \frac{1}{x-1}\le L\le \frac{1}{x} \right)\]\[\Rightarrow \] \[0\le L\le 0\]\[\Rightarrow \] \[L=0\] |
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