(1) Write a short essay on this topic, using examples: Why is it that we need to consider reparametrizations of a curve? Why have we chosen arclength as the “correct” parametrization? What is arclength, and how do we go about using it? How practical is reparametrization by arclength?
(2) Reparametrize the curve below by arclength: α(t) = (e ^t cos(t), e^t sin(t), e^t )