Prove that f (x) = x^3 - 1000x^2 + x - 1 is ω (x^3) and o (x^3).

Question

Jayleen Joseph

Mathematics

15 June, 20:06

Prove that f (x) = x^3 - 1000x^2 + x - 1 is ω (x^3) and o (x^3).

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Remington Marshall · Answer 1

F (x) = x 3 - 1000x^2 + x - 1

> x3 - 1000x^ 2

= (x - 1000) x^2

> (.9x) x^2

=.9x^3

Therefore, f (x) is Ω (x^3) with C =.9, k = 10, 000. Also, for all x > 0:

f (x) = x^3 - 1000x^2 + x - 1

< x^3 + 1000x^3 + x^3 + x^3

= 1002x^3

Therefore, f (x) is O (x^3) with C = 1002, k = 1.