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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A least integer $n$ such that $f(x)$ is $O(x^n)$ for each of the following functions. Arrange according to the value of $n$ in increasing order.
Solution
Find dominant growth for each.
A:
$3x^3+(\log x)^4$
Dominant term = $x^3$
$n=3$
B:
$(x^5+x^2+1)/(x^3+1) \approx x^2$
$n=2$
C:
$(x^3+x^2+1)/(x^2+1) \approx x$
$n=1$
D:
$(x^2+5\log x)/(x^2+1) \approx 1$
$n=0$
Thus:
D → $O(1)$
C → $O(x)$
B → $O(x^2)$
A → $O(x^3)$
Increasing order:
D, C, B, A
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