Level Curves and Contour Maps

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8 Terms

1
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level curve(s) of a fn

the level curve of a fn f(x,y) of 2 vars are cruves w eqn f(x,y) = k where k is a real number in the RANGE of f(x,y)

2
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contour map

a collection of level curves

3
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tangent plane

a tangent plane approximates a SURFACE at a POINT on the SURFACE/plane (unlike a tangent line which approximates a CURVE at a pt on a CURVE)

4
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formula for tangent plane

  • derived from the LINEARIZATION of f(x,y) at the point (x0,y0)

  • this is the tangent plane approximation of f at (x0,y0)

<ul><li><p>derived from the LINEARIZATION of f(x,y) at the point (x0,y0)</p></li><li><p>this is the tangent plane approximation of f at (x0,y0)</p></li></ul><p></p>
5
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the eqn of the tangent plane to the graph of a fn of two vars at the pt (a,b,f(a,b)) is:

the eqn is known as the LINEAR APPROXIMATION or the TANGENT PLANE APPROXIMATION

<p>the eqn is known as the LINEAR APPROXIMATION or the TANGENT PLANE APPROXIMATION</p>
6
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differentials

<p></p>
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if both fx and fy are continuous, f(x,y) is

differentiable

8
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dz, dy, dx

increment of z (small change in z2 and z1, or delta z), increment of y, increment of x