Use a CAS to perform the following steps in
Chapter 12, Problem 38CE(choose chapter or problem)
Use a CAS to perform the following steps in Exercises \(35–38\).
Plot the space curve traced out by the position vector \(r\).Find the components of the velocity vector \(d r / d t\).Evaluate \(d r / d t\) at the given point and determine the equation of the tangent line to the curve at \(r\left(t_{0}\right)\).Plot the tangent line together with the curve over the given interval.
\(r(t)=\left(\ln \left(t^{2}+2\right)\right) i+\left(\tan ^{-1} 3 t\right) j+\sqrt{t^{2}+1} k,-3 \leq t \leq 5, t_{0}=3\)
Equation Transcription:
Text Transcription:
35-38
r
dr/dt
r(t_0)
r(t) = (ln (t^2 + 2))i + (tan^-1 3t)j + sqrt t^2 + 1 k, -3 leq t leq 5, t_0 = 3
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