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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\frac{1}{x}}}}}{{{e^{\left( {\frac{1}{x} + 1} \right)}}}} = $
  • A
    $0$
  • B
    $1$
  • C
    Does not exist
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) $\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{e^{1/x}}}}{{{e^{\left( {\frac{1}{x} + 1} \right)}}}} = \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{e^{1/x}}}}{{{e^{\frac{1}{x}}}.e}}$

$ = \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{1}{e} = {e^{ - 1}}$.

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