Level Curves and Visualization of Surfaces

Example: Draw several level curves for the graph of f(x,y) = y e^2x .

Strategy: Set y e^2x = C and let C take on the values 1, 2, 5

y = C e ^{˗ 2x}

So y(x) = e ^{˗ 2x} y(x) = 2 e ^{˗ 2x} y(x) = 5 e ^{˗ 2x}

Then plot each level curve as shown below.

Click here for another example.

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