Thread: Sketch z = arctan(x^2 + y^2)

Sketch the level curves for . What does the graph of the function look like?

Attempt:

Let x = k:

1.

Let y = k:

2.

Let z = k:

3.

Now what I am not sure of is how would you draw 1-3? Would you have to use all the steps for curve sketching e.g. first derivative, second derivative etc?

Take in booth sides. For example in 3) : (circumference) .


Fernando Revilla

How would you plot from 2)?

The level curves occur when the function

a constant. This gives

As noted above this gives

This is the equation of a circle centered at the origin with radius

Oh so by level curves the question actually means you must just let z = k (not x = k and y = k) and hence draw that graph?