1. Find the maximum height above the xy-plane achieved by the function r(t) = (et, sint, t(4 – t)).
1. Find the maximum height above the xy-plane achieved by the function r(t) = (et, sint, t(4 – t)).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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![1. Find the maximum height above the xy-plane achieved by the function
r(t) = (e¹, sin t, t(4 – t)).
Prove that this height is the maximum.
2. Prove the following:
d
[r • (r' × r")] = r. · (r′ × r").
dt
3. The binormal vector of a function r(t) is defined as B = T × N, where
r'(t)
||r' (t)||
is the unit tangent vector and
T(t)
N(t)
T'(t)
||T'(t)||
is the unit normal vector.
Find the binormal vector for r(t) = (cost, sint, 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2Ff85c8623-c22d-4734-a742-e04faa1ceb28%2Fn3arvhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the maximum height above the xy-plane achieved by the function
r(t) = (e¹, sin t, t(4 – t)).
Prove that this height is the maximum.
2. Prove the following:
d
[r • (r' × r")] = r. · (r′ × r").
dt
3. The binormal vector of a function r(t) is defined as B = T × N, where
r'(t)
||r' (t)||
is the unit tangent vector and
T(t)
N(t)
T'(t)
||T'(t)||
is the unit normal vector.
Find the binormal vector for r(t) = (cost, sint, 0).
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