Download presentation

Presentation is loading. Please wait.

Published byArely Disney Modified over 2 years ago

1
13.7 Tangent Planes and Normal Lines for an animation of this topic visit http://www.math.umn.edu/~rogness/multivar/tanplane_withvectors.shtml

2
Recall from chapter 11: Standard equation of a plane in Space a(x-x 1 ) + b(y-y 1 ) + c (z – z 1 ) = 0 parametric form equations of a line in space:x = x 1 + at y = y 1 +bt z = z 1 +ct symmetric form of the equations of a line in space x-x 1 = y – y 1 = z – z 1 a b c

3
Example 1 For the function f(x,y,z) describe the level surfaces when f(x,y,z) = 0,4 and 10

4
Example 1 solution For the function f(x,y,z) describe the level surface when f(x,y,z) = 0,4 and 10

6
For animated normal vectors visit: http://www.math.umn.edu/~rogness/math2374/paraboloid_normals.html OR http://www.math.umn.edu/~rogness/multivar/conenormal.html http://www.math.umn.edu/~rogness/math2374/paraboloid_normals.html http://www.math.umn.edu/~rogness/multivar/conenormal.html

7
Example 2 Find an equation of the tangent plane to given the hyperboloid at the point (1,-1,4)

8
Example 2 Solution:

9
Example 3 Find the equation of the tangent to the given paraboloid at the point (1,1,1/2)

10
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

11
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)

12
Example 4 Solution Find a set of symmetric equations for the normal line to the surface given by xyz = 12 At the point (2,-2,-3)

13
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

Similar presentations

OK

Parametric Surfaces and their Area Part II. Parametric Surfaces – Tangent Plane The line u = u 0 is mapped to the gridline C 2 =r(u 0,v) Consider the.

Parametric Surfaces and their Area Part II. Parametric Surfaces – Tangent Plane The line u = u 0 is mapped to the gridline C 2 =r(u 0,v) Consider the.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on cross-sectional study design Ppt on product specification Ppt on nuclear power generation Ppt on viruses and anti viruses names Ppt on autonomous car sensors Ppt on dc motor drives Ppt on forward rate agreement pdf Ppt on rational numbers for class 8 free download Ppt on trade related intellectual property rights Ppt on great indian scientists