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12. limits — MATHS STD 11 Science — Question

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

Answer

Correct option: D.
$1$
d
(d) $\mathop {\lim }\limits_{x \to 0} \,\,\frac{{{{\tan }^{ - 1}}x}}{x}$,   $\left( {\frac{0}{0}\,{\rm{form}}} \right)$

$ = \mathop {\lim }\limits_{x \to 0} \,\frac{{\frac{1}{{1 + {x^2}}}}}{1} = \mathop {\lim }\limits_{x \to 0} \,\,\frac{1}{{1 + {x^2}}} = \frac{1}{{1 + 0}} = 1$.

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