Find r'(t), r(t,), and r'(to) for the given value of to. r(t) = (1 + t)i + t°j, to = 1 r'(t) = r(t,) = r'(t,) = Sketch the curve represented by the vector-valued function, and sketch the vectors r(t,) and r'(to). y 3 3 r' 2- r' (1, 2) 2 (0, 1) (0, 1) -1 1(1, 0) -3 -2 -1 (0, -1) -2 (-1, 0) -1 -21 r" 2 (2, 1) (1, 0)

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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Find r'(t), r(t,), and r'(t,) for the given value of to:
r(t) = (1 + t)i + t³j, to
= 1
r'(t)
r(t,) =
r'(t,)
%D
Sketch the curve represented by the vector-valued function, and sketch the vectors r(to) and r'(t).
y
4
y
3
y
4
3
3
r'
2
(1, 2)
2
(0, 1)
1
(0, 1)
r'
X
-2
-1
1(1, 0)
2
X
-3
-2
1
(0, – 1)
-2
1
2
(-1, 0)
-1
-2
y
3
r'
2
(2, 1)
1
X
-1
2
(1, 0)
-1/
3.
II
Transcribed Image Text:Find r'(t), r(t,), and r'(t,) for the given value of to: r(t) = (1 + t)i + t³j, to = 1 r'(t) r(t,) = r'(t,) %D Sketch the curve represented by the vector-valued function, and sketch the vectors r(to) and r'(t). y 4 y 3 y 4 3 3 r' 2 (1, 2) 2 (0, 1) 1 (0, 1) r' X -2 -1 1(1, 0) 2 X -3 -2 1 (0, – 1) -2 1 2 (-1, 0) -1 -2 y 3 r' 2 (2, 1) 1 X -1 2 (1, 0) -1/ 3. II
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