MCQ
The function which is continuous for all real values of $x$ and differentiable at $x = 0$ is
- A$|x|$
- B$\log x$
- ✓$sin\ x$
- D${x^{\frac{1}{2}}}$
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$\frac{d y}{d x}=1+x e^{y-x},-\sqrt{2}\,<\,x\,<\,\sqrt{2}, y (0)=0$ then, the minimum value of $y(x)$ , $\mathrm{x} \in(-\sqrt{2}, \sqrt{2})$ is equal to:
$\alpha \log _{\mathrm{e}}|1+\tan \mathrm{x}|+\beta \log _{\mathrm{c}}\left|1-\tan \mathrm{x}+\tan ^{2} \mathrm{x}\right|+\gamma \tan ^{-1}\left(\frac{2 \tan \mathrm{x}-1}{\sqrt{3}}\right)+\mathrm{C}$
when $\mathrm{C}$ is constant of integration, then the value of $18\left(\alpha+\beta+\gamma^{2}\right)$ is .... .