Problem 1. (a) (b) t = 0. Let F(u, v) = (tan(u — 1) — eº, u² — v²) and G(x, y) = (eª−y, x − y). Calculate D(Fo G)(1, 1) using the chain rule, i.e., without computing Fo G directly. Let (t) = (et + t², cos(t) + 2t). Find the unit tangent vector to the curve (FoGoc) (t) when

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 1.
(a)
(b)
t = 0.
Let F(u, v) = (tan(u − 1) — eº, u² − v²) and G(x, y) = (ex−y, x − y).
-
Calculate D(Fo G)(1, 1) using the chain rule, i.e., without computing F o G directly.
Let c(t) = (et + t², cos(t) + 2t). Find the unit tangent vector to the curve (Fo Goc)(t) when
Transcribed Image Text:Problem 1. (a) (b) t = 0. Let F(u, v) = (tan(u − 1) — eº, u² − v²) and G(x, y) = (ex−y, x − y). - Calculate D(Fo G)(1, 1) using the chain rule, i.e., without computing F o G directly. Let c(t) = (et + t², cos(t) + 2t). Find the unit tangent vector to the curve (Fo Goc)(t) when
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