MCQ
Let $A = \int\limits_0^1 \, \frac{{{e^t}\,\,\,d\,t}}{{1\,\, + \,\,t}}$ then $\int\limits_{a - 1}^a {\,\,\frac{{{e^{ - t}}\,dt}}{{t\, - \,a\, - \,1}}} $ has the value
- A$Ae^{-a}$
- ✓$-Ae^{-a}$
- C$-ae^{-a}$
- D$Ae^a$
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$STATEMENT$ $-1: \overline{\mathrm{PQ}} \times(\overline{\mathrm{RS}}+\overline{\mathrm{ST}}) \neq \overrightarrow{0}$. because
$STATEMENT$ $-2: \overline{\mathrm{PQ}} \times \overline{\mathrm{RS}}=\overrightarrow{0}$ and $\overline{\mathrm{PQ}} \times \overline{\mathrm{ST}} \neq \overrightarrow{0}$.
$g(x)=\left\{\begin{array}{cl}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\1, & x=-1\end{array} \text { and } h(x)=2[x]-f(x),\right.$
where $[x]$ is the greatest integer $\leq x$. Then the value of $\lim _{x \rightarrow 1} g(h(x-1))$ is