>>18
On the contrary. They are using limits to describe how it is impossible to divide by 0. This is because it will appear to converge to a certain x-value, but then will suddenly become a vertical asymptote. Thus, there is an infinite limit. That is +-infinity. The very fact that it does not converge to a specific y-value, proves that it is impossibe to divide by zero.
Also, if you take an inverse of a function, you will effectively change its range and domain. Thereby your explaination with linear function is extremely inadequate. Consider dividing higher polynomials or rational functions by 0 (something which is easily described by limits).