# Gradient, Divergences, and Curl

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).

https://brainmass.com/math/graphs-and-functions/gradient-divergences-curl-526491

#### 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 ...

#### Solution Summary

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