Multivariable Calculus 16 | Taylor's Theorem [dark version]

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This video is about Taylor polynomials in several variables.

#MultivariableCalculus
#Analysis
#Integral
#Calculus
#Derivatives
#Mathematicspdt
#Lagrange

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[yashchadda]

Two questions from this: If the goal of the taylor series is to approximate a function at a point, why is it necessary to find quadratic and higher order approximations if the linear approximation (tangent line) gives you the function's value at the point? Also, why is it by taking the second derivative you get a quadratic approximation?

[martinbranson]

How are you writing it? What software is it you are taking notes on? Great video!

[piero]

Theres no restriction over the norm of the limit yes? I mean, it can be any norm?