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Re: Big O Proof
Posted:
May 10, 2013 2:04 PM



For all c, k, n there exists x>k suct that tan(x)>cn^n:
Pick a positive integer m so that m*pi>k. Suppose n>1.
 lim_{x>m*pi+pi/2 from below} tan(x) / (c*n^x)  <=  [ lim_{x>m*pi+pi/2 from below} tan(x) ] / (c*n^x)  since c*n^x is increasing. The denominator is finite and the numerator tends to +infinity, therefore the fraction must become >1.
If tan(x) were O(n) for n<=1 then tan(x) would also be O(n+2) therefore the proof for n>1 is sufficient.
Just for fun: can you prove that tan(x) is not O(tan(tan(x)) but sin(x) is O(sin(sin(x))?
________________________________ From: Nicolas Manoogian <discussions@mathforum.org> To: discretemath@mathforum.org Sent: Thursday, May 9, 2013 10:58 PM Subject: Big O Proof
You guys have been awesome. I have one last proof this year and my professor is not letting up! I'm trying to prove that tan(x) is not Big O of n^x. My professor doesn't like my undefined argument.
He responded to my proof: "Given c,k,n find s > k such that tan(x) > cn^x."
He also added: "Don't forget case when n<=1!"
Now, do I want to be using limits? I really thought that I had the right solution!
Thanks! Nic



