Show that \(x^{2}+4 x+17\) is \(O\left(x^{3}\right)\) but that \(x^{3}\) is not \(O\left(x^{2}+4 x+17\right)\)

Step 1 of 2

Let us assume that x > 1 then

So, the first term that is will influence.

Then, instead of we can write as . Because will grow as slow as

And the second term is also an influence because x will grow as slow as

Hence,

Where n = 3, C = 22 and k = 1

So the growth of the function is O().

Hence, it is proved that has the growth of function O().