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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
Range of the function $f (x) =$ $\left[ {\frac{1}{{\ln ({x^2} + e)}}} \right]\,\, + \,\,\frac{1}{{\sqrt {1 + {x^2}} }}\,$  is , where $[*]$ denotes the greatest integer function and $e =$ $\mathop {Limit}\limits_{\alpha  \to 0} {(1 + \alpha )^{1/\alpha }}\,$
  • A
    $\left( {0,\,\frac{{e + 1}}{e}} \right)$  $\cup \{2\}$
  • B
    $(0, 1)$
  • C
    $(0, 1] \cup \{2\}$
  • ✓
    $(0, 1) \cup \{2\}$
✓

Answer

Correct option: D.
$(0, 1) \cup \{2\}$
d
$\left[ {\frac{1}{{\ln ({x^2} + e)}}} \right]\, - \left[ \begin{gathered}  0\,\,\,\,x\, \ne \,0 \hfill \\   1\,\,\,\,\,x\, = \,0 \hfill \\ \end{gathered}  \right.$ 

 $f(x) - \left[ \begin{gathered}   2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \,0 \hfill \\  \frac{1}{{\sqrt {1 + {x^2}} }}\,\,\,\,x \ne 0 \hfill \\  \end{gathered}  \right.$
Hence range of $f (x)$ is $(0, 1) \cup {2}$

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