Answer to Question #264790 in Discrete Mathematics for Gracie Zhou

Question #264790

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.


1
Expert's answer
2021-11-14T16:41:33-0500

f(x)=(xlogx)24(xlogx)2+4(xlogx)2=5(xlogx)25x4f(x) = (xlogx)^2 - 4\le (xlogx)^2 +4 (xlogx)^2 =5 (xlogx)^2 \le5x^4

f(x)=O(x4)f(x)=O(x^4)


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)=\infin

g(x)O(x4)g(x)\neq O(x^4)


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