Long description: Fig3717

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The image displays two separate graphs, (a) and (b), showing sets of contour lines labeled with different constant values.

Alt text: The image displays two separate graphs, (a) and (b), showing sets of contour lines labeled with different constant values.

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  • On the left graph, labeled (a), the contour lines are straight lines with a positive slope, representing contours for the function \(x+y\).
  • These lines are labeled with constant values such as \(\phi = 1\), \(\phi = 2\), \(\phi = 3\), \(\phi = 4\), and \(\phi = 5\), indicating that the level curves are parallel lines moving upwards from the \(x\)-axis.
  • On the right graph, labeled (b), the contour lines are concentric closed curves centered around the origin, representing contours for the function \(9-x^2 -y^2\).
  • These contours are also labeled with constant values, including \(\phi = 0\), \(\phi = 5\), and \(\phi = 8\), forming nested ellipses or circles.

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