State the definition of “f(x) is O(g(x))” and use the definition to show that x 2...

Question

Question

State the definition of “f(x) is O(g(x))” and use the definition to show that x 2 + 3x is O(x 3 ).

Please show as much work as possible. Thanks.

Answer 1

Answer #1

Definition: The function

iff .

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Given,

f(x) = x² + 3x

g(x) = x³

As

So, it is enough to show that x³ grows faster than any other power of x.

Multiply with x on the right hand and then take a constant "c".

Answer 2

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