Question

Are the following sequences well ordered as ε → 0? If not, arrange them so that they are:

(b) Φ1=ε^5e^-3/ε, Φ2=ε, Φ3=εln(ε), Φ4=e^-ε, Φ5=(1/ε)sin(ε^3), Φ6=1/ln(ε)

(c) Φ1=e^ε-1-ε, Φ2=e^ε-1, Φ3=e^ε, Φ4=e^ε-1-ε-(1/2)ε^2

PLEASE ANSWER PARTS B & C (primarily part b). I know they are not well ordered, but I'm not sure how to order them. Thanks!

1. Are the following sequences well ordered as e -> 0? If not, arrange them so that they are. [sinh(e/2)]2n for n = 0,1,2, 3,.. (а) фп (b) 1ee-3/e, ¢2 sin(e3) 4e eln(e), Фе - In(e) Ф2 Фз = €, (c) 1e -1 e, ¢4 = e - 1 - 2 p2= ee - 1, e - 1, ¢s e, 3= ee, 04 = e - 1 - e - (d) n= e-1/e for n = 0,1,2,3, ...

Answer 1

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