As mentioned in the text, the tangent line to a smooth curve r(t) = (t)i + g(t)j

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As mentioned in the text, the tangent line to a smooth curve r(t) = ƒ(t)i + g(t)j + h(t)k at t = t0 is the line that passes through the point (ƒ(t0), g(t0), h(t0)) parallel to v(t0), the curve’s velocity vector at t0. Find parametric equations for the line that is tangent to the given curve at the given parameter value t = t0.

r(t) = (sin t)i + (t2 - cos t)j + etk, t0 = 0

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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