Let C be the space curve with the parametrization r(t) = (cost, sint, In (cost)) for - < t < 4. (a) Find the unit tangent vector T(t) of C at the point (1,0,0). (b) Find the unit normal vector N(t) of Cat (1,0,0). (c) Find the curvature of Cat (1,0,0).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let C be the space curve with the parametrization r(t) = (cost, sint, ln(cost)) for - <
t<.
(a) Find the unit tangent vector T(t) of C at the point (1,0,0).
(b) Find the unit normal vector N(t) of Cat (1,0,0).
(c) Find the curvature & of Cat (1,0,0).
(d) Use the previous parts to describe the osculating circle of Cat (1,0,0).
Transcribed Image Text:Let C be the space curve with the parametrization r(t) = (cost, sint, ln(cost)) for - < t<. (a) Find the unit tangent vector T(t) of C at the point (1,0,0). (b) Find the unit normal vector N(t) of Cat (1,0,0). (c) Find the curvature & of Cat (1,0,0). (d) Use the previous parts to describe the osculating circle of Cat (1,0,0).
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