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Tangent and Arc Length

# Tangent and Arc Length - ME 210 Applied Mathematics for...

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ME 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 The tangent to a curve C at a point A on it is defined as the limiting position of the straight line L through A and B, as B approaches A along the curve as illustrated in the Figure. Here, it is assumed that the curve C is represented by a continuously differentiable (i.e., derivative exists and is continuous) vector function , where t is some parameter, the points A and B correspond to t and t + Δt . Then the straight line L has the direction of the vector Tangent and Arc Length of a Curve ) t ( r ) t ( r ) t t ( r r

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ME 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 ) t ( r ) t ( r ) t t ( r ) t ( r A B Tangent L O x y z C ) t ( T Δs: Arc Length from A to B Tangent to a Curve ) t ( r ) t t ( r r