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What is arc length parametrization?

Answer 1

Luke Alvarez

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Answer 2

Emilia Aguilar

Arc length parametrization is a method used to represent a curve in such a way that the parameter used to describe the curve corresponds to the length of the curve itself. In other words, instead of using arbitrary parameters such as ( t ) or ( s ), which may not have a direct relationship with the distance along the curve, arc length parametrization employs a parameter that reflects the actual distance traveled along the curve. This parametrization is particularly useful in various mathematical and scientific contexts, such as in differential geometry, physics, and computer graphics, where precise measurements of distances along curves are needed.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.