As mentioned in the text, the tangent line to a smooth curve r(t) = f(t)i + g(t)j + h(t)k at t = to is the line that passes through the point (f(to), g(to), h(to)) parallel to v(to), the curve's velocity vec- tor at to. In Exercises 19-22, find parametric equations for the line that is tangent to the given curve at the given parameter value t = to. 20. r(t) = t² i + (2t − 1)j + t³k, to = 2
As mentioned in the text, the tangent line to a smooth curve r(t) = f(t)i + g(t)j + h(t)k at t = to is the line that passes through the point (f(to), g(to), h(to)) parallel to v(to), the curve's velocity vec- tor at to. In Exercises 19-22, find parametric equations for the line that is tangent to the given curve at the given parameter value t = to. 20. r(t) = t² i + (2t − 1)j + t³k, to = 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Tangents to Curves
As mentioned in the text, the tangent line to a smooth curve
r(t) = f(t)i + g(t)j + h(t)k at t = to is the line that passes through
the point (f(to), g(t), h(t)) parallel to v(to), the curve's velocity vec-
tor at to. In Exercises 19-22, find parametric equations for the line that
is tangent to the given curve at the given parameter value t = to.
20. r(t) = t² i + (2t − 1)j + t³k, to = 2
sin t)j
t ln t k.
(sin 2)k
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