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Use the definition of $ "f(x) is O (g(x)) $ to show that $ x^4+9x^3 + 4x+7 is O(x^4) $

My answer was :

I used divide and conquer

$ x^4 \le cx^4 , when\; c = 1 $

$ 9x^3 \le cx^4 , when \; c=9 \; and \; x\gt 1$

$ 4x \le cx^4 , when \; c=4 \; and \; x=1$

$7 \le cx^4 , when \; c=17 \; and \; x>1$

so $ x^4 + 9x^3+4x+7 \le x^4+9x^4+4x^4+7x^4$

$x^4+9x^3+4x+7 \le 31x^4 $

so $ x^4+9x^3+4x+7 \le cx^4 ,when \; c=31 \; and \; k =1 $

Is my answers correct ? And if it's correct, is there any other solution ?

Out Of Bounds
  • 1,531
  • The notation $k$ seems to have appeared out of nowhere in the last line; presumably it's intended to be the lower end of the range of $x$'s for which the inequality holds. Apart from that, the proof looks correct, though I'm not sure why you used 17 where 7 would do. – Andreas Blass Nov 11 '13 at 01:55
  • Oh sorry that's 7 not 17.And thanks for your help ! – Out Of Bounds Nov 11 '13 at 02:41

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