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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
The value of $\left[ {\frac{{\log \left( {\frac{x}{e}} \right)}}{{x - \,e}}} \right]\,\forall x\, > \,e$ is equal to (where [.] denotes greatest integer function)
  • A
    $1$
  • ✓
    $0$
  • C
    $2$
  • D
    does not take unique value
✓

Answer

Correct option: B.
$0$
b
$\frac{\log x-\log \mathrm{e}}{x-e}=\frac{1}{c} c \in(e, x)(L M V T)$

$\Rightarrow 0<\frac{\log \left(\frac{x}{e}\right]}{x-e}<1$

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