1. Consider the vector-valued function F(t) = sin(2t) t (2, 1, -2), a) Find the domain of F. b) Show that is continuous at t = 0. t ' 1 - V₁ +1) " +t , et, t #0 t = 0.
1. Consider the vector-valued function F(t) = sin(2t) t (2, 1, -2), a) Find the domain of F. b) Show that is continuous at t = 0. t ' 1 - V₁ +1) " +t , et, t #0 t = 0.
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
![1. Consider the vector-valued function
F(t) =
sin(2t)
t
(2, 1, -2),
a) Find the domain of F.
b) Show that F is continuous at t = 0.
;
et,
t
1-√1+t,
t #0
t = 0.
= (1/2/3/17, -2).
2. Consider the vector-valued function R(t) with R(1) = (1,2,−1) and R (t) = (1
a) Find '(1) if (t) = (-2, -3t, t²) × R'(t).
b) Find the equation of the normal plane to the graph of Ả at t = 1.
c) Find the arc length of the graph of R from the point at t = 1 to the point at t = 3.
d) Find the curvature of the graph of R at t = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3793f3d7-bee1-497e-96fc-dc6876135f1e%2F2d66e914-c86e-4b93-83da-1200ee6db90c%2Fwx62ao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the vector-valued function
F(t) =
sin(2t)
t
(2, 1, -2),
a) Find the domain of F.
b) Show that F is continuous at t = 0.
;
et,
t
1-√1+t,
t #0
t = 0.
= (1/2/3/17, -2).
2. Consider the vector-valued function R(t) with R(1) = (1,2,−1) and R (t) = (1
a) Find '(1) if (t) = (-2, -3t, t²) × R'(t).
b) Find the equation of the normal plane to the graph of Ả at t = 1.
c) Find the arc length of the graph of R from the point at t = 1 to the point at t = 3.
d) Find the curvature of the graph of R at t = 1.
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