Am I correct with these problems for Big-O, Big-Theta, Big-Omega or neither? These are the problems:


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*$x^{x^2}$ and $ 2^{2^x}$

*$\cos(x)$ and $\tan(x)$

*$x^3$ and $x$
My answers are: 


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*$x^{x^2}$ is O($ 2^{2^x} $)

*Neither Big O, nor Big Omega, nor Big Theta

*$x^3$ is Big-Omega($x$)


Are these correct answers?

Here's a table, showing the general idea:
1.lim x^{x^2}/2^{2^x}
the limit is 0
because x^{x^2}/2^{2^x} = x^2 log x / 4^x => x^3/4^x so x^{x^2} is o(2^{2^x}) bucuase exponential functions grows faster than polynomials
2.lim cos(x)/tan(x) for this lim 1/sin(x) and lim sin(x) doesn't exist and
we want x→∞ so this Periodic function doesn't have a big O notation . 
3.for lim x^3/x we have infinity so x^3 is small omega (x) and  () = (()) ⇒ () = Ω(), because Big Omega is used to indicate that  ≥  
