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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
$\lim_\limits{\text{x} \rightarrow 1}{1−\text{x}+[\text{x}+1]+[1−\text{x}]}$, where $[x]$ denotes greatest integer function, is
  • A
    $0$
  • ✓
    $1$
  • C
    $-1$
  • D
    $2$
✓

Answer

Correct option: B.
$1$
Substitute $x = 1 + t$
$ \text{L.H.S} \lim_\limits{\text{t}\rightarrow o^{-}} (-\text{t}+[2+\text{t}]+[-\text{t}])$
$= 0 + 1 + 0 = 1$
$ \text{R.H.S} \lim_\limits{\text{t}\rightarrow o^{-}} (-\text{t}+[2+\text{t}]+[-\text{t}])$
$= 0 + 2 - 1 = 1$
$\text{L.H.S = R.H.S}$

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