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A topographical map contains curved lines called contour lines. Each contour line corresponds to the points on the map that have equal elevation (Figure 1). A level curve of a function of two variables [latex]f\,(x,\ y)[/latex] is completely analogous to a counter line on a topographical map.
Level Curves and Contour Plots. Level curves and contour plots are another way of visualizing functions of two variables. If you have seen a topographic map then you have seen a contour plot. Example: To illustrate this we first draw the graph of z = x2 + y2. On this graph we draw contours, which are curves at a fixed height z = constant.
A level curve of a function of two variables f (x, y) f (x, y) is completely analogous to a contour line on a topographical map. Figure 4.7 (a) A topographical map of Devil’s Tower, Wyoming. Lines that are close together indicate very steep terrain.
Graphs of Surfaces and Contour Diagrams - 2 Suppose the function h looks like this: Then, the contour diagram of the function h is a picture in the (x;y){plane showing the contours, or level curves, connecting all the points at which h has the same value. Thus, the equation h(x;y) = 100 gives all the points where the function value is 100.
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A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. [1][2] It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of ...
points on the graph for each elevation z = c, and then you project the curves on the graph onto the xy-plane. In the example below, we nd the contour corresponding to the elevation z = 100. The contour happens to consist of two separate pieces: Below are contour maps for some common graphs. Example 2. Here is a paraboloid z = x2 + y2 and its ...
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The gure below shows how the contour diagram from the corn production example is related to the graph of the corn production function C= f(R;T). Contour lines, or level curves, are obtained from a surface by slicing it with horizontal planes. A contour diagram is a collection of level curves labeled with function values.
