The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0 < x < \frac{\pi}{2}$, then general solution of the differential equation is

Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is

The values of $a$ and $b$, so that the function

$$f(x)= \begin{cases}x+\mathrm{a} \sqrt{2} \sin x & , 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b & , \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ \mathrm{a} \cos 2 x-\mathrm{b} \sin x & , \frac{\pi}{2}< x \leq \pi\end{cases}$$

is continuous for $0 \leq x \leq \pi$, are respectively given by