The relative rates of tending towards infinity of different functions?

In my reading, it says that the function $x/\log x$ approaches infinity slower than $x$ (I got that bit), but then it says that it also approaches it faster that the functions $x^{1-d}$, where $d$ is any positive integer, as (apparently) evidenced by the limit of $(\log x)/x^d$ approaching $0$. That's where I get lost. From my interpretation, the functions $x^{1-d}$ are $x^0$, $x^{-1}$, $x^{-2}$, etc.. These approach $0$, not infinity (excluding $x^0$, obviously), so DUH, of course $x/\log x$ approaches infinity faster! Or am I missing something?

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reading what, exactly? The first part works when $0 < d < 1$ is not an integer at all. Instead of the letter $d,$ it is more common to use the Greek $\delta$ for this. –  Will Jagy Jul 17 '12 at 19:03