13.7 tangent planes and normal lines for an animation of this topic visit...
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13.7 Tangent Planes and Normal Linesfor an animation of this topic visit
http://www.math.umn.edu/~rogness/multivar/tanplane_withvectors.shtml
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Recall from chapter 11: • Standard equation of a plane in Space• a(x-x1) + b(y-y1) + c (z – z1) = 0• parametric form equations of a line in
space: x = x1 + at
y = y1 +bt
z = z1 +ct• symmetric form of the equations of a line
in space• x-x1 = y – y1 = z – z1
• a b c
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Example 1
For the function f(x,y,z) describe the level surfaces when f(x,y,z) = 0,4 and 10
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Example 1 solutionFor the function f(x,y,z) describe the level surface
when f(x,y,z) = 0,4 and 10
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For animated normal vectors visit:http://www.math.umn.edu/~rogness/math2374/paraboloid_normals.htmlORhttp://www.math.umn.edu/~rogness/multivar/conenormal.html
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Example 2
Find an equation of the tangent plane to given the hyperboloid at the point (1,-1,4)
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Example 2 Solution:
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Example 3
Find the equation of the tangent to the given paraboloid at the point (1,1,1/2)
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Example 3 Solution: Find the equation of the tangent to the given paraboloid at the point (1,1,1/2). Rewrite the function as f(x,y,z) = - z
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Example 4
Find a set of symmetric equations for the normal line to the surface given by
xyz = 12
At the point (2,-2,-3)
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Example 4 SolutionFind a set of symmetric equations for the normal
line to the surface given by
xyz = 12 At the point (2,-2,-3)
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One day in my math class, one of my students spent the entire period standing leaning at about a 30 degree angle from standing up straight. I asked her “Why are you not standing up straight? “
She replied “Sorry, I am not feeling normal.”
Of course that students name was Eileen.
- Mr. Whitehead