Calc 3 14.4 Notes: Tangent Planes and Linear Approximations

Objectives:
7. Define the total differential.
8. Use the total differential to approximate the change in a function.
Ch 14 playlist: • Calculus 3 Chapter 14:...
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[@onlyramizz3688]

perfect!!!

[@nguyenquoctran8423]

why is x=x0; y=y0 a plane. I thought it's a line ? e.g: x = 3; y = 5 is a line parallel to Oz and can have any z value. thank you

[@alexandraniedden5337]

x=# and y=# both represent lines in 2-space. Picture the line x=3 on the xy-plane. When we consider the equation x=3 in 3-space, that line then "goes up and down" with z forming a plane.