Solution Found!
Show that x2 + 4x + 17 is O(x3) but that x3 is not O(x2 +
Chapter 2, Problem 9E(choose chapter or problem)
QUESTION:
Show that \(x^{2}+4 x+17\) is \(O\left(x^{3}\right)\) but that \(x^{3}\) is not \(O\left(x^{2}+4 x+17\right)\)
Questions & Answers
QUESTION:
Show that \(x^{2}+4 x+17\) is \(O\left(x^{3}\right)\) but that \(x^{3}\) is not \(O\left(x^{2}+4 x+17\right)\)
ANSWER: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(
).