2. Sample Papers
  3. KVPY

KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    \[\underset{x\,\to \,0}{\mathop{\text{Limit}}}\,\,\,\frac{{{\log }_{e}}[x]}{x}\] where [ ] denotes the greatest integer function is:

    A) 0         

    B) 1

    C) \[-1\]

    D) non-existent

    Correct Answer: A

    Solution :

    \[L=\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}\]
    \[\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}\le L\le \underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,x}{x}\]
    \[\underset{x\,\to \,\infty }{\mathop{Limit}}\,\left( \frac{1}{x-1}\le L\le \frac{1}{x} \right)\]\[\Rightarrow \]      \[0\le L\le 0\]\[\Rightarrow \]            \[L=0\]


You need to login to perform this action.
You will be redirected in 3 sec spinner