When it is even then both the limits from the right (positives) and limits from the left (negatives) are the same because you raise it to an even power. Thus, they approach positive infinite.
However, when it is odd the limits from the right remain positive and approach infinite. While the limits from the left remain negative and approach negative infinite.
That is wrong.lim(x->0) 1/x^2 = 0 ... why?