Coreman: Relative Asymptotic growths

Question

Suppose
$A = log^{k}n$
$B = n^{\epsilon} $
 Assume that $ k\geq 1$  and $ \epsilon > 0$
What is the relation b/w the asymptotic time complexities of A and B?
1. A  = O(B)
2. A = o(B)
3. A = $\Omega (B)$
4. A = $\omega (B)$

Comments

@aghori positive integers mentioned in question.

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@saxena0612 It would have been $o(B)$ had the $\epsilon>1$

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Got it !

Answer 1

Solved by @joshi_nitish

PS: A = small-oh(B) is the best choice.

Comments

@manu but since it is an increasing function and more specifically strictly increasing why it can't be both small and big O ? i

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When it's small-oh then it will have to be big-oh!!  in this question A = o(B)

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Yes, that what I am asking in this particular answer what @joshi_nitish has mentioned is it small or big?
From my point of view, small o is the best choice .

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yes small-o is strongest answer!