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    Unit tangent and unit normal vectors.

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    Given the vector r(t) = t i + t^2 j find T(t), T(1) a dn then N (1).
    After this I am to sketch the plane curve and graph the vectors T(1) and N(1) at t = 1.

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    https://brainmass.com/math/vector-calculus/unit-tangent-unit-normal-vectors-69929

    Solution Preview

    Solution:

    r(t) = t i + t^2 j

    First we find the unit tangent vector

    T(t) = (i+2tj)/ sqrt(1+4t^2)

    Now use the quotient rule to find T '(t)

    T'(t) = (1+4t^2)^1/2 (2j) - (i+2tj) 4t (1+4t^2)^ -1/2
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    Solution Summary

    Unit tangent and unit normal vectors are investigated. The solution is detailed and well presented.

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