the space curve (t) = (2t, t², 2t)
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:1. Draw the osculating plane at (2, 1, 2)
2. Draw the osculating circle at (2, 1, 2)

Transcribed Image Text:The space curve \(\vec{r}(t) = \langle 2t, t^2, 2t \rangle\) represents a parametric equation where the curve is described by the vector function \(\vec{r}(t)\). In this expression:
- \(2t\) represents the x-component of the vector.
- \(t^2\) represents the y-component of the vector.
- \(2t\) represents the z-component of the vector.
This curve is parametrized by \(t\), where \(t\) typically represents time or another independent variable. The point on the curve at any given time \(t\) is given by substituting \(t\) into the vector function, providing the corresponding x, y, and z coordinates.
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