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1 Oct 2016
 Derivatives of Vector Functions; The Unit Tangent Vector; Arc Length; The Arc Length For example, consider the 2-dimensional space curve defined by
 The derivative of a vector valued function gives a new vector valued function that is tangent to the defined curve. The analogue to the slope of the tangent line is the direction of the tangent line. Since a vector contains a magnitude and a direction, the velocity vector contains more information than we need.
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 Example11.4.2Computing the unit tangent vector. Let ?r(t)=?3cos(t) tangent vector. Note: these are the same problems as in Exercises 11.4.4.5 — 11.4.4.8.
 The unit tangent vector is then, Example 2 Find the vector equation of the tangent line to the curve given by at . First we need the tangent vector and since this is the function we were working with in the previous example we can just reuse the tangent vector from that example and plug in .
 Example: Find the unit tangent and unit normal vectors, tangential and normal components of the curve x = t ? sint, y = 1 ? cost at t = ?. 2 . Solution: The position
 Home · Calculators · Calculus III Calculators · Math Problem Solver (all calculators). Unit Tangent Vector Calculator. The calculator will find the unit tangent
 3 Mar 2014
 demos > ma215 > 13_3TNBFrames > examples. Math 215 Examples . The unit tangent vectors are graphically intuitive, as we are used to thinking about
     
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