91Ó°ÊÓ

Compute the gradient \(\nabla f\). $$ f(x, y)=\frac{1}{x^{2}+y^{2}} $$

Find the points on the circle \(x^{2}+y^{2}=100\) which are closest to and farthest from the point \((2,3) .\)

Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid $$ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=1 $$

Find the equation of the tangent plane to the surface \(z=f(x, y)\) at the point \(P\). \(f(x, y)=x+2 y, P=(2,1,4)\)

Find \(\frac{\partial f}{\partial x}\) and \(\frac{\partial f}{\partial y}\). $$ f(x, y)=\sqrt{x^{2}+y^{2}} $$