MCQ
$\mathop {\lim }\limits_{x \to a} \frac{{({x^{ - 1}} - {a^{ - 1}})}}{{x - a}} = $
- A$1/a$
- B$\frac{{ - 1}}{a}$
- C$\frac{1}{{{a^2}}}$
- ✓$\frac{{ - 1}}{{{a^2}}}$
$= \mathop {\lim }\limits_{x \to a} \,\frac{{ - 1}}{{ax}} = \frac{{ - 1}}{{{a^2}}}$.
Or $\mathop {\lim }\limits_{x \to a} \,\,\frac{-1/{{x}^{2}}-0}{1-0}$
(By Appling $L-$ Hospital’s rule)
$-\frac{1}{{{a}^{2}}}$
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$f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right) \text {, where } x \in\left[0, \frac{\pi}{2}\right] \text {, }$
consider the following two statements :
($I$) $\mathrm{f}$ is increasing in $\left(0, \frac{\pi}{2}\right)$.
($II$) $\mathrm{f}^{\prime}$ is decreasing in $\left(0, \frac{\pi}{2}\right)$.
Between the above two statements,