MATH 2203 –Quiz 3 (Version 2) Solution
February 18, 2008
NAME________________________________
The curve r(t) = tcos (t)i+tsin (t)j,tis pictured below.
Graph of r(t) = tcos (t)i+tsin (t)j,t
Show that the curvature of this curve at the point (0;0) is 2.
Solution: The point (0;0) corresponds to t= 0. The curvature at this
point is given by
(0) = jr0(0) r00 (0)j
jr0(0)j3.
Note that
r0(t) = (tsin (t) + cos (t)) i+ (tcos (t) + sin(t)) j
r00 (t) = (tcos (t)2 sin (t)) i+ (tsin (t) + 2 cos(t)) j
so
r0(0) = i
r00 (t) = 2j.
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