Section 14.1
Worksheet by Jim Brown
For this worksheet we graph some functions $z = f(x,y)$ and some level curves.
(x, y, z) (x, y, z) |
Example 1: The first example we graph is the function $z = 5 \cos (x - y)$.
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Example 2: The next we graph is $z = \frac{5\cos(x)\sin(y)}{2 + \tan(xy)}$.
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Example 3: We now graph $z = |x|$.
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Example 4: Here we graph the level curves of the function $z = y - \ln(x)$. First we graph the function in blue with the curves with constant $z$ value. The second graph is the level curves in the $xy$-plane.
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Example 5: Here we graph the function and then the level curves of $z = \frac{1}{2 + x^2 + y^2}$. Note how the level curves get closer together as the graph gets steeper.
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