Tangent Planes and How to Build Them
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- čas přidán 22. 08. 2021
- Tangent lines were important in single variable calculus because they give a good way to approximate a complicated function with a simple function near a given point. Similarly, tangent planes give a good way to approximate complicated 2-variable functions with a simple function, but how do you set up the equation for a tangent plane?
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This video was funded by Texas A&M University as part of the Enhancing Online Courses grant.
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The animations in this video were mostly made with a homemade Python library called "Morpho". You can find the project here:
github.com/morpho-matters/mor...
"Explain it to me like i'm five" done correctly, thanks a lot!
This was a concise and insightful explanation, bravo!
This probably saved me a lot of time, thanks! You made it very easy to understand
This video is a really nice review. Thank you
Cramming for finals you're a big help man thanks so much
thank you so much. it's so helpful 🥰
nice and easy explanation
well done, thank you
After long search ultimately I got the answer of the junction point of single variable to double variable that leads to multivariable view point of grad and tangent point. Many thanks. Kindly upload a video of direction of the gradient and actual line of ascent on the surface with an example (with 3D graph) of an paraboloid. ❤from 🇮🇳🙏.
Thank you❤
9th grade has been killing me so far thank you so much!!!
how the hell are u taking multivariable calculus in 9th grade
@@quacki614 I take that when I am 1st grade
No, two independent lines do not uniquely define a plane. In three-dimensional space, a plane is defined by at least three non-collinear points. The reason is that a single line can be drawn through any two points, and multiple lines can be parallel to each other while lying in different planes.
To uniquely determine a plane, you need three points that are not collinear (meaning they are not on a single straight line). These three points can then be used to form a unique plane in three-dimensional space.
What we do in multi variable calculus is take 3 points, form 2 vectors with them and then take the cross product to find a normal to both of them. Then we use one point, the one they both share in common, and plug them in to the equation of a plane. The vector will be a,b,c… and the point will be x0,y0,z0….
Apparently a plane is defined by a vector normal to the plane and a point on the plane.
Hreo!
excellent