Q1. By computing appropriate Lipschitz constants, show that the following functions Saisty Lipschitz condition on the sets D indicated: g(t.u)=4²+², on D: iris 1.lul 1. (b) g(t.u) cosu+usin't, on D: "Pilds1.lu) 1. < and on D:0 stsa, lul<, (here a>0 is a constant)
Q1. By computing appropriate Lipschitz constants, show that the following functions Saisty Lipschitz condition on the sets D indicated: g(t.u)=4²+², on D: iris 1.lul 1. (b) g(t.u) cosu+usin't, on D: "Pilds1.lu) 1. < and on D:0 stsa, lul<, (here a>0 is a constant)
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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Transcribed Image Text:Q1. By computing appropriate Lipschitz constants, show that the following functions satisfy
Lipschitz condition on the sets D indicated:
Vg(t.u)=4t+u², on D: iti s 1. jul 1.
(b) g(t,u) t cos u+ usin³t, on D: Its 1. jul<
(c) g(t.u)=teti, on D:ltis 1.lul <ce and on D:0 sts a, lul < (here a>0 is a constant)
Q2. Show that the following functions do not satisfy the Lipschitz condition in the region indicated
(a) g(t.u)-sinu-g(0.u)=0 on D:ltl s 1, ul<
(b) g(t.u)=9(t,0)=0,on D: It ≤ 2. Jul
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