Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 29E
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![Concept 6: Properties of Vector Functions (continued)
(c) Find S G(t) dt
Derivative Properties of Vector-Valued Functions
For F(t) = (f(t), g(t), h(t)) where f(t), g(t), h(t) are differentiable functions,
(1)
F'(t) = (f'(t), g'(t), h'(t))
(2)
S F(t) dt = (S f(t) dt, ſ g(t) dt, ſ h(t) dt)
(3)
lim F(t) = (lim f (t), lim g(t), lim h(t))
t-a
t→a
t-a
t-a
(4) [F(t) + G(t)] = F'(t) + G'(t)
(5) [CF(t)] = cF'(t)
(6)
Ip(t)F(t)] = p'(t)F(t) + p(t)F'(t)
dt
(7)
[F(t) • G(t)] = F'(t) • G(t) + F(t) • Gʻ(t)
dt
(8)
[F(t) x G(t)] = F'(t) × G(t) + F(t) x G'(t)
%3D
dt
(9)
(F(p(t)) = F'(p(t)p'(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb72669-0680-48fe-8aa6-56d86c073f3c%2F3e04863d-0d69-47d9-b65d-eda9608c4fb4%2Fwnsk93g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Concept 6: Properties of Vector Functions (continued)
(c) Find S G(t) dt
Derivative Properties of Vector-Valued Functions
For F(t) = (f(t), g(t), h(t)) where f(t), g(t), h(t) are differentiable functions,
(1)
F'(t) = (f'(t), g'(t), h'(t))
(2)
S F(t) dt = (S f(t) dt, ſ g(t) dt, ſ h(t) dt)
(3)
lim F(t) = (lim f (t), lim g(t), lim h(t))
t-a
t→a
t-a
t-a
(4) [F(t) + G(t)] = F'(t) + G'(t)
(5) [CF(t)] = cF'(t)
(6)
Ip(t)F(t)] = p'(t)F(t) + p(t)F'(t)
dt
(7)
[F(t) • G(t)] = F'(t) • G(t) + F(t) • Gʻ(t)
dt
(8)
[F(t) x G(t)] = F'(t) × G(t) + F(t) x G'(t)
%3D
dt
(9)
(F(p(t)) = F'(p(t)p'(t)
![[M R N] Concept 6: Properties of Vector Functions
Let F(t) = t-4 i-5j+ (2t – 4t³) k and G(t) = 2 cos t i+ e-5t j – sin 4t k.
(a) Find (F(t) • G()]
(b) Given p(t) = 3VE , evaluate [p(t)F(t)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb72669-0680-48fe-8aa6-56d86c073f3c%2F3e04863d-0d69-47d9-b65d-eda9608c4fb4%2Fx99fct_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[M R N] Concept 6: Properties of Vector Functions
Let F(t) = t-4 i-5j+ (2t – 4t³) k and G(t) = 2 cos t i+ e-5t j – sin 4t k.
(a) Find (F(t) • G()]
(b) Given p(t) = 3VE , evaluate [p(t)F(t)]
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