I have two questions here.

I must prove that [tex]f(n) = 100n^2 + 5n + 10[/tex] is in big-O of [tex]g(n) = n^3 - 100n^2[/tex]

I already found a constant [tex]c[/tex] and an [tex]n[/tex] that satisfies the condition such that [tex]f(n) \leq c * g(n)[/tex]. Let [tex]c = 1[/tex] and [tex]n = 201[/tex].

However, I am stuck on showing/manipulating the algebra that this is true.

Second question:

How would you prove this? I know you use the triangle inequality, but I have no idea how to implement this. Any help would be great, thanks.

If [tex]f[/tex] in big-O of [tex]g[/tex] then [tex]|f - g|[/tex] in big-O [tex]g[/tex]

I must prove that [tex]f(n) = 100n^2 + 5n + 10[/tex] is in big-O of [tex]g(n) = n^3 - 100n^2[/tex]

I already found a constant [tex]c[/tex] and an [tex]n[/tex] that satisfies the condition such that [tex]f(n) \leq c * g(n)[/tex]. Let [tex]c = 1[/tex] and [tex]n = 201[/tex].

However, I am stuck on showing/manipulating the algebra that this is true.

Second question:

How would you prove this? I know you use the triangle inequality, but I have no idea how to implement this. Any help would be great, thanks.

If [tex]f[/tex] in big-O of [tex]g[/tex] then [tex]|f - g|[/tex] in big-O [tex]g[/tex]

Last edited: