Using the definition of "Big-O" determine if each of the following functions, f(x) = (xlogx)^2 - 4 and g(x) = 5x^5 are O(x^4) and prove your claims.
f(x)=(xlogx)2−4≤(xlogx)2+4(xlogx)2=5(xlogx)2≤5x4f(x) = (xlogx)^2 - 4\le (xlogx)^2 +4 (xlogx)^2 =5 (xlogx)^2 \le5x^4f(x)=(xlogx)2−4≤(xlogx)2+4(xlogx)2=5(xlogx)2≤5x4
f(x)=O(x4)f(x)=O(x^4)f(x)=O(x4)
limx→∞(g(x)/x4)=limx→∞(5x5/x4)=∞\displaystyle{\lim_{x\to \infin}}(g(x)/x^4)=\displaystyle{\lim_{x\to \infin}}(5x^5/x^4)=\infinx→∞lim(g(x)/x4)=x→∞lim(5x5/x4)=∞
g(x)≠O(x4)g(x)\neq O(x^4)g(x)=O(x4)
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