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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 1} \frac{{1 + \log x - x}}{{1 - 2x + {x^2}}} = $
  • A
    $1$
  • B
    $-1$
  • C
    $0$
  • ✓
    $ - \frac{1}{2}$
✓

Answer

Correct option: D.
$ - \frac{1}{2}$
d
(d) Applying $ L- $Hospital’s rule,

$\mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{1 + \log x - x}}{{1 - 2x + {x^2}}} = \mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{\frac{1}{x} - 1}}{{ - 2 + 2x}} = \mathop {{\rm{lim}}}\limits_{x \to 1} \,\,\frac{{1 - x}}{{2x(x - 1)}}$

Again applying $ L-$ Hospital’s rule,

$\mathop {{\rm{lim}}}\limits_{x \to 1} \frac{{ - 1}}{{4x - 2}} = - \frac{1}{2}$.

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