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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).

    © BrainMass Inc. brainmass.com June 4, 2020, 3:39 am ad1c9bdddf
    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.

    $2.19

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