13.3_matb_113_notes_e.doc
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13.3 Arc Length and Unit Tangent Vector T
Definition Length of A smooth Curve
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The length of a smooth curve , that is traced exactly once as t increases from t =a to t =b , is
Arc Length Formula
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Example:1 Find the length of the curve
Arc Length Parameter with base Point
Speed on a Smooth Curve Definition: Unit Tangent VectorThe unit tangent vector of a smooth curve
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is T =
Example:2 Given Find (i) the length of the curve within the given t interval. (ii) the unit tangent vector of the curve .
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