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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty } [x({a^{1/x}} - 1)]$,$(a > 1) = $
  • A
    $\log x$
  • B
    $1$
  • C
    $0$
  • ✓
    $ - \log \frac{1}{a}$
✓

Answer

Correct option: D.
$ - \log \frac{1}{a}$
d
(d) $\mathop {\lim }\limits_{x \to \infty } x\,({a^{1/x}} - 1) = \mathop {\lim }\limits_{x \to \infty } \,\left[ {\frac{{{a^{1/x}} - 1}}{{1/x}}} \right]$

$ = \mathop {\lim }\limits_{x \to \infty } \frac{{[{e^{{{\log }_e}{a^{1/x}}}} - 1]}}{{1/x}} = {\log _e}a = - {\log _e}\frac{1}{a}.$

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