1. Consider the vector-valued functionF(t) =sin(2t)t(2, 1, -2),a) Find the domain of F.b) Show that F is continuous at t = 0.;et,t1-√1+t,t #0t = 0.= (1/2/3/17, -2).2. Consider the vector-valued function R(t) with R(1) = (1,2,−1) and R (t) = (1a) 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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Answered: 1. Consider the vector-valued function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.