Is This Statement True?

Question

Is it correct to assert that $T(n) \in \Theta(n^2)$ when:

$$ \frac{n^2}{\log{(n)}} \leq T(n) \leq \frac{n^2}{\log{(n)}} + n $$

Answer 1

No it's not correct according to this definition since the sequence $\left(\frac1{\log n}\right)$ is convergent to $0$ so we can't find $k_1>0$ such that $$k_1\le \frac1{\log n},\quad \forall n\ge n_0$$