$\mathrm{The} \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{squares} \mathrm{of} \mathrm{two} \mathrm{positive} \mathrm{numbers} \mathrm{is} 200 \mathrm{then} \mathrm{their} \mathrm{minimum} \mathrm{product} \mathrm{is}$

If $\mathrm{f}(\mathrm{x},\mathrm{y})=\mathrm{y} \sin \left(\mathrm{xy}\right)$ then the value of ${\mathrm{f}}_{\mathrm{x}}(\mathrm{\pi },1)$ is _____.

The value of $\underset{(\mathrm{x},\mathrm{y})\to (0,0)}{\lim } \frac{{\mathrm{x}}^2-\mathrm{xy}}{\sqrt{\mathrm{x}}-\sqrt{\mathrm{y}}}$ is _____.

A point $\left(\mathrm{a},\mathrm{b}\right)$ is said to be a saddle point of f(x, y), if at $\left(\mathrm{a},\mathrm{b}\right)$

$\underset{(\mathrm{x},\mathrm{y})\to (0,0)}{\lim }\frac{{\mathrm{x}}^2-\mathrm{yx}}{\mathrm{x}+\mathrm{y}}=$ _____.

The equation of tangent plane of surface z = x at point (2,0,2) is _____.

The value of the limit $\underset{(\mathrm{x}, \mathrm{y})\to (0, 0)}{\lim }\frac{2{\mathrm{x}}^2\mathrm{y}}{ {\mathrm{x}}^4+{\mathrm{y}}^2 }$ is _____.

The equation of the tangent plane to the surface $2{\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{z}=3$ at point (2,1,-3) is _____.

Conditions for $\mathrm{f}(\mathrm{x},\mathrm{y})$ to have a maximum values are _____.

The function ${\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}+10$ has minimum value at point _____.