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(a) Find [F(t) • G(t)] (b) Given p(t) = 3VE , evaluate [p(t)F(t)] dt

(a) Find [F(t) • G(t)] (b) Given p(t) = 3VE , evaluate [p(t)F(t)] dt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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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)
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)]
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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