"Solution:Given (x3 +2x)/(2x + 1) is O(x2)
To satisfy the definition of O(x2),
we need to find an appropriate choice of c
and k.
Let consider x ≥ 1000 and reason by inequalities:
=>(x3+ 2x)/(2x + 1)<(x3 + 2x)/2x=1/2 x2 + 1 <1/2x2 + x2 =3/2x²<br>
Since
(x3+2x)/(2x+1) < 3/2x2 when x ≥ 1000, we can choose k = 1000 and
c = 3/2 .
hence
(x3 + 2x)/(2x + 1) is O(x2)"
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