28-29. Unit tangent vectors Find the unit tangent vector T(t) for the following parameterized curves. Then determine the unit tangent vector at the given value of t. 28. r(t) = (8, 3 sin 2t, 3 cos 2t), for 0 < t < n; t =1/4 29. r(t) = (2e', e", t), for 0 < t < 2n; t = 0 %3D 30-31. Velocity and acceleration from position Consider the following position functions.
28-29. Unit tangent vectors Find the unit tangent vector T(t) for the following parameterized curves. Then determine the unit tangent vector at the given value of t. 28. r(t) = (8, 3 sin 2t, 3 cos 2t), for 0 < t < n; t =1/4 29. r(t) = (2e', e", t), for 0 < t < 2n; t = 0 %3D 30-31. Velocity and acceleration from position Consider the following position functions.
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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Question
#28
Transcribed Image Text:(ot* i + 4t j +
20.
dt
sin at i+j+
k dt
1+t2
er
21.
22-24. Derivative rules Suppose u and v are differentiable functions at t =0
with u(0) = (2, 7, 0), u'(0) = (3, 1, 2), v(0) = (3,-1, 0), and
v'(0) = (5, 0, 3). Evaluate the following expressions.
d
22.
(u v)t=0
dt
d
-(u x v) t=0
23.
dt
d
24.
dt
(u(et.
25-27. Finding r from r' Find the function r that satisfies the given
conditions.
25. r'(t) = (1, sin 2t, sec? t); r(0) = (2, 2, 2)
26. r'(t) = (e', 2e", 6e*); r(0) = (1, 3, – 1)
27. r'(t) =
4
2t + 1, 3t2
?); r(1) = (0, 0, 0)
1+t2 '
28-29. Unit tangent vectors Find the unit tangent vector T(t) for the following
parameterized curves. Then determine the unit tangent vector at the given
value of t.
28. r(t) = (8, 3 sin 2t, 3 cos 2t), for 0 < t < n; t = T/4
29. r(t) = (2e', e2", t), for 0 < t < 2n; t = 0
30-31. Velocity and acceleration from position Consider the following
position functions.
a. Find the velocity and speed of the object.
b. Find the acceleration of the object.
30. r(t) = (t +1, t2 + 10t
3
for t >0
31. r(t) = (e" +1, e*
1
et+1
for t >0
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