Use the definition of the fact that f(x) is O(g(x)) to show that:
1. 7x^2 is O(x^2)
2. x^4 + 9x^3 + 4x + 7 is O(x^4)
3. (x^2+1) / (x+1) is O(x) Hint: Try to simplify algebraic expression.
`Hey,
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1)
Let f(x)=7*x^2
So,
f(x)<=8*x^2 for all x>=1
So, we found c=8 and x0=1
So,
f(x)=O(x^2)
2)
Let f(x)=x^4 + 9x^3 + 4x + 7
So,
f(x)=x^4 + 9x^3 + 4x + 7<=x^4+9*x^4+4*x^4+7*x^4=21*x^4 for x>=1
So, we found a constant c=21 and x0=1
So,
f(x)=O(x^4)
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