Level Curves and Cross Sections
Main Concept
A level curve of the surface is a two-dimensional curve with the equation , where k is a constant in the range of f. A level curve can be described as the intersection of the horizontal plane with the surface defined by f. Level curves are also known as contour lines.
A vertical cross section (parallel to a coordinate plane) of a surface is a two-dimensional curve with either the equation or the equation , where c and d are constants. Such a cross section can be described as the intersection of a vertical plane or with the surface defined by f.
Both level curves and cross sections are helpful for visualizing and plotting multivariate functions.
Select a function from the drop-down menu or type your own function in the text box below and click "Enter" to plot it. Click the radio buttons to view either a level curve or a cross section. Use the slider to change the value of the related constant , , or . Click "Reset" to reset both plots.
z = f(x, y) =
Enter Functionx^2 + y^2 - 5x^2 - y^2sqrt(100 - x^2)-2*sqrt(x^2 + y^2) + 8x - x^3/12 - y^2/4cos(x) - sin(y)2*sin(x) + cos(y)ln(abs(x)) + yexp(x) - exp(y)cos(x)sin(cos(x*y))sin(x*cos(y))exp(sin(x + y))
=
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