Question

Show that (x3 + 2x)/(2x + 1) is O(x2).

Answer 1

me assume thats spozed tu be . . . (x^3+2x) / (2x+1) . . . or bout x^3/2x.... x^3/x=x^3*x^-1 =x^2 . . . .

Answer 2

"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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