Consider the following position function in the plane: ř (t) = (t3 – 3t)i + 3t?j. %3D For this vector-valued function, assume as given that 7'(t) = (3t2 – 3)ï + 6tj and that then 7(2) = 2ỉ + 12j and 7 ' (2) = 9ỉ + 12j %3D The graph below is part of the graph of 7 (t). Sketch r (2) on the graph, labeling the point at its head (terminal point), Also, sketch on the graph a vector parallel to 7'(2), in the same direction as 7'(2), and with the same tail (initial point) at 7 '(2) , i.e., with its initial point at the terminal point of 7 (2). However, your vector and ř' (2) need not have the same magnitude. 22 20 y 18 16 14 12 10 6 4 2 -10 -5 10 -2 -4 -6 -8 -10 -12 -14
Consider the following position function in the plane: ř (t) = (t3 – 3t)i + 3t?j. %3D For this vector-valued function, assume as given that 7'(t) = (3t2 – 3)ï + 6tj and that then 7(2) = 2ỉ + 12j and 7 ' (2) = 9ỉ + 12j %3D The graph below is part of the graph of 7 (t). Sketch r (2) on the graph, labeling the point at its head (terminal point), Also, sketch on the graph a vector parallel to 7'(2), in the same direction as 7'(2), and with the same tail (initial point) at 7 '(2) , i.e., with its initial point at the terminal point of 7 (2). However, your vector and ř' (2) need not have the same magnitude. 22 20 y 18 16 14 12 10 6 4 2 -10 -5 10 -2 -4 -6 -8 -10 -12 -14
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3.
Consider the following position function in the plane:
r(t) = (t³ - 3t)i + 3t²j.
For this vector-valued function, assume as given that
ř'(t) = (3t² − 3)ỉ + 6t]
and that then (2) = 27 + 12j and 7'(2) = 97+ 12j
The graph below is part of the graph of r (t). Sketch (2) on the graph,
labeling the point at its head (terminal point), Also, sketch on the graph a vector
parallel to '(2), in the same direction as '(2), and with the same tail (initial
point) at 7 '(2), i.e., with its initial point at the terminal point of 7 (2).
However, your vector and 7' (2) need not have the same magnitude.
22
20 Y
18
16
14+
12-
10-
6-
2
10
15
-10
-2
-4
-6
-8+
-10-
-12+
-14
-5
X
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3b99fb6-e1d2-4611-bd89-4973efdce514%2F5e761a57-9d56-4660-bfb9-56b6bbfc1cbd%2F3z3g6je_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Consider the following position function in the plane:
r(t) = (t³ - 3t)i + 3t²j.
For this vector-valued function, assume as given that
ř'(t) = (3t² − 3)ỉ + 6t]
and that then (2) = 27 + 12j and 7'(2) = 97+ 12j
The graph below is part of the graph of r (t). Sketch (2) on the graph,
labeling the point at its head (terminal point), Also, sketch on the graph a vector
parallel to '(2), in the same direction as '(2), and with the same tail (initial
point) at 7 '(2), i.e., with its initial point at the terminal point of 7 (2).
However, your vector and 7' (2) need not have the same magnitude.
22
20 Y
18
16
14+
12-
10-
6-
2
10
15
-10
-2
-4
-6
-8+
-10-
-12+
-14
-5
X
20
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