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Homework Statement
α(t) = (sint, cost + ln tan t/2) for α: (0:π) -> R2
Show that α is a smooth, parametrized curve, which is regular except for t = π/2
The Attempt at a Solution
I am familiar with the definitions of smooth and regular, which I have provided below, however I am unsure as to how to formally show what the question asks.
Am I supposed to show that dα/dt at t=π/2 is zero and hence not regular?
for what it's worth, I have computed dα/dt at t=π/2 and it is = 0!
Smooth - a function α(t) = α1(t), α2(t)...αn(t) is smooth if each of its components α1, α2,...,αn of α is smooth, that is, all the derivatives dαi/dt, d2α/dt2... exist for i = 1,2,...,n
Regular - a curve is regular if all its points are regular, that is dα/dt is nonzero.
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