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Gradient, Divergences, and Curl

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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).

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Solution Summary

The expert examines gradient, divergences and curls. The normal line to the level curve of the surface is determined.

Solution Preview

Two things:
1. Here I use the standard vector notations where e_x is a unit vector in the x direction, e_y is a unit vector in the y direction and e_z ...

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