# Additional exercises 2

## Exercise

Let

## Exercise

Let

## Exercise

Let

## Exercise

Determine the directional derivative,

## Exercise

Compute the Jacobian matrix of the transformation

## Exercise

Consider the functions,

Let *Out of curiosity, try to understand what curve traces out as varies.*

## Exercise

Let

and

line | value |
---|---|

What does this say about

## Exercise

Consider the surface

*Hint: write this surface as a level set , calculate at the specified point and use the known connection between gradient and tangent plane.*