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Let F(t)= (-5t² +2,-5e-3, 3 sin(2t)) = 0. Round to 4 decimal places. Find the unit tangent vector T(t) at the point t T(0) =

Let F(t)= (-5t² +2,-5e-3, 3 sin(2t)) = 0. Round to 4 decimal places. Find the unit tangent vector T(t) at the point t T(0) =

Advanced Engineering Mathematics
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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**Question 7** Let \(\vec{r}(t) = \langle -5t^2 + 2, -5e^{-3t}, 3 \sin(2t) \rangle\). Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). Round to 4 decimal places. \(\vec{T}(0) =\) [Input Box] Question Help: [Video Button] [Check Answer Button]
Transcribed Image Text:**Question 7** Let \(\vec{r}(t) = \langle -5t^2 + 2, -5e^{-3t}, 3 \sin(2t) \rangle\). Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). Round to 4 decimal places. \(\vec{T}(0) =\) [Input Box] Question Help: [Video Button] [Check Answer Button]
Expert Solution
Step 1: Given:

r with rightwards arrow on top open parentheses t close parentheses equals open angle brackets negative 5 t squared plus 2 comma space minus 5 e to the power of negative 3 t end exponent comma space 3 space sin open parentheses 2 t close parentheses close angle brackets

We have to find unit tangent vector T with rightwards arrow on top open parentheses t close parentheses at a point t equals 0.

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