Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t), t²) on the interval [0, π]. (b) Find parametric equations for the tangent line to the curve C at the point where t = π/6.
Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t), t²) on the interval [0, π]. (b) Find parametric equations for the tangent line to the curve C at the point where t = π/6.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Question 3
The parametrization of a curve \( C \) is given by \( \mathbf{r}(t) = \langle \sin(t), \cos(t), t^2 \rangle \) on the interval \([0, \pi]\).
(a) Find \( \mathbf{r}'\left(\frac{\pi}{6}\right) \).
(b) Find parametric equations for the tangent line to the curve \( C \) at the point where \( t = \frac{\pi}{6} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6b79a9-c663-4f87-993a-883a678be91b%2Fd8b3dbfa-d12b-4e86-a7c3-4b5a71bdb7ca%2Fbzd0cmd_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 3
The parametrization of a curve \( C \) is given by \( \mathbf{r}(t) = \langle \sin(t), \cos(t), t^2 \rangle \) on the interval \([0, \pi]\).
(a) Find \( \mathbf{r}'\left(\frac{\pi}{6}\right) \).
(b) Find parametric equations for the tangent line to the curve \( C \) at the point where \( t = \frac{\pi}{6} \).
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