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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...