Scalar Field

A scalar field is a function of several variables of the type

Which takes in a multi-dimensional vector and outputs a scalar
With the domain

And the image

Level Set

The level set for a scalar field is the set of all input values that output

Example

The level set of is a circle

Plan to solve limits

  1. Check continuity (plug it in)
  2. Check a few paths
    1. Any two paths differ then the limit DNE
    2. The limit can not be proved to exist via exhaustion
  3. Try Polar Coordinates
Solving limits via polar cordinate