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math.HO2019
Arc length of function graphs via Taylor's formula
Patrik Nystedt
We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subd…
math.HO2019
Poisson's fundamental theorem of calculus via Taylor's formula
Patrik Nystedt
We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is…