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Parameterization of Curves

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See attachment for equation and full problem set.

a) Find a parametric representation of the tangent line to the curve C2 at t = 1
b) Derive the equation of the normal plane to the curve C2 at t = 1, of this form
ax + by +cz = d

c) Find the distance of the plan in (b) and the origin (0,0,0)
d) Find the speed of the curve C2 as a function of t
e) Find the length of the curve C2 (between t = 0 and t = 2)

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Solution Summary

The solution shows in detail how to find a tangent to a parameterized curve, the normal plane, the distance to the plane and the length of the curve.