- #1
Mr Davis 97
- 1,462
- 44
For example, say we have ##\frac{x^4(x - 1)}{x^2}##. The function is undefined at 0, but if we cancel the x's, we get a new function that is defined at 0. So, in this case, we have ##x^2(x - 1)##, then ##x^2(x - 1)(1)##, and since ##\frac{x^2}{x^2} = 1##, we then have ##\frac{x^4(x - 1)}{x^2}##. However, this is a new function, since the domain has changed to exclude x = 0. How is this justified? Why can we go about changing the function in that way. Specifically, when we evaluate limits, in the case where we have ##\frac{x^4(x - 1)}{x^2}##, how to we know that cancelling the x's will lead to the correct limit, since that is in effect the limit of the function ##x^2(x−1)## and not ##\frac{x^4(x - 1)}{x^2}##?