Gradient:
1. Find the gradient of the function f : x^2y/ z at the point M(-2;3;4).
What is the directional derivative of this function in the direction of vector I =(12;-4;3)?
2. Find the gradient of the scalar function f = cos(|r|^n) , Where
r : (X, y, Z).
Write the result as a function of r
3. Find the normal line to the level curve of the surface given by
X^2 + 3y^2/2 = 7 at point M(2;-1).
Divergence:
4. Calculate the divergence of the vector Q : (X^2, y^3, XZ^3) at the field:point (A1,1,3).
Curl:
5. Calculate the curl of the vector field: a = (Z^2, X^2, y^2) at the point A(1,2,3)
6. Calculate curl(r/r^n)
Use of the "nabla" symbol (V):
7. Find a gradient of scalar product of two vector fields F(x,y,z) and G(x,y,Z).