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Consider the function ϕ(x,y) = x2 + y2. (1 pt) Find the gradient field for ϕ(x,y)....

Consider the function ϕ(x,y) = x2 + y2.

  1. (1 pt) Find the gradient field for ϕ(x,y).
  2. (1 pt) Describe the level cuves of ϕ(x,y).
  3. (2 pts) Sketch some level curves of ϕ(x,y) as well the gradient field.
  4. (1 pt) What do you notice about the relationship between the level curves and the gradient field?
Math   Calculus   
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