Determine whether $x^{3}$ is $O(g(x))$ for each of these functions $g(x) .$ a) $g(x)=x^{2}$ b) $g(x)=x^{3}$ c) $g(x)=x^{2}+x^{3}$ d) $g(x)=x^{2}+x^{4}$ e) $g(x)=3^{x}$ f) $g(x)=x^{3} / 2$
Added by Philip G.
Step 1
We need to find a constant $c > 0$ and a value $x_0$ such that $|x^3| \le c|x^2|$ for all $x > x_0$. However, as $x$ grows, $x^3$ will always be greater than $x^2$, so we cannot find such a constant $c$. Show more…
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