Gradient Vector, Tangent Planes, and Normal Lines

Practice Questions

Calculus 3 › Gradient Vector, Tangent Planes, and Normal Lines

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1

Find the gradient, $\bigtriangledown F$ , of the function .

2

Find $\bigtriangledown F$ of the function .

3

Find the gradient, $\bigtriangledown F$ , of the function .

4

Find the gradient vector for the following function:

5

Find the gradient vector of the following function:

$f(x,y,z)=x^2+x+4+y^2\sin(z^2)$

6

Find the equation of the plane tangent to the following function at :

$f(x,y,z)=z^3\ln(y)+\frac{x^2}{2}$

7

Find the gradient vector of the following function:

$f(x,y,z)=x+y\cos(z^2)+z^3$

8

Find the equation of the tangent plane to the following function at :

$f(x,y,z)=xy\sin(x)+z$

9

Find the equation to the tangent plane to the following function at the point :

$f(x, y, z)=\ln(xy^2z^3)$

10

Find of the following function:

$f(x,y,z)=\sec(xyz^2)$

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