3-8 (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for anto the g given value of t. 3. r(t) = (t = 2, t² + 1), t = -1 fox 4. r(t) = (t², t³), t= 1 5. r(t) = e²¹ i + e'j, t = 0 ( NOUSICS 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 cos tj, t = 3π/4 15+ me 8. r(t) = (cost + 1)i + (sin t - 1)j, t = -π/3 BauOW (17 9-16 Find the derivative of the vector function dar
3-8 (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for anto the g given value of t. 3. r(t) = (t = 2, t² + 1), t = -1 fox 4. r(t) = (t², t³), t= 1 5. r(t) = e²¹ i + e'j, t = 0 ( NOUSICS 6. r(t) = e'i + 2tj, t = 0 7. r(t) = 4 sin ti - 2 cos tj, t = 3π/4 15+ me 8. r(t) = (cost + 1)i + (sin t - 1)j, t = -π/3 BauOW (17 9-16 Find the derivative of the vector function dar
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...
Related questions
Question
7 please
Transcribed Image Text:2. (a) Make a large sketch of the curve described by the vector
function r(t) = (t², t), 0 ≤ t ≤ 2, and draw the vectors
r(1), r(1.1), and r(1.1) - r(1).
(b) Draw the vector r'(1) starting at (1, 1), and compare it
with the vector
qey
Explain why these vectors are so close to each other in
length and direction.
3-8
#10
(a) Sketch the plane curve with the given vector equation.
(b) Find r'(t).
(c) Sketch the position vector r(t) and the tangent vector r'(t) for
and
the given value of t.
o ulubled to visi Laine
04-108
r(1.1) - r(1)
0.1
-
3. r(t) = (t = 2, t² + 1), t =
4. r(t) = (t², t³), t = 1
21
101
5. r(t) = e²¹ i + e'j, t = 0
or 15/1
12. r(t) =
=
nonsoon Seu SW (01 (19
6. r(t) = e'i + 2t j, t = 0
7. r(t) = 4 sin ti - 2 cos tj, t = 3π/4
8. r(t) = (cost + 1)i + (sin t - 1)j, t = -π/3
-1
9-16 Find the derivative of the vector function.
9. r(t)=(√2, 3, 1/1²)
10. r(t) = (e¹, t - t³, In t)
11. r(t) = t² i + cos (t2) j + sint k
1
1 + t
i+
t
1 + t
++++
1²
j+ - k
1 + t
200
14
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Expert Solution
Step 1
Introduction:
The derivative of a vector-valued function can be understood to be an instantaneous rate of change.
To take the derivative of a vector-valued function, take the derivative of each component.
Given: vector equation.
To find:
Derivative of the given equation. And the graphs.
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