Which function grows faster: N log N or N1+ε / log N, ε > 0?

N logN grows faster.

Explanation:

In N1+∈/N logN logN is the denominator. So this term is constantly getting divided by logN while in N logN there is no term in the division and for N > 2 log N will be > 1. So N logN will gorw faster. Since ∈ is greater than 0 So the numerator will be greater than N but it will not grow as fast as N logN.