>>13278035>>13276078This is bullshit. You should be able to divide out regardless of whether you’ve simplified or not - all you’re doing is using substitution. The problem with this problem is that you can’t divide by 0, and the expression 0/0 is an indeterminate form.
So the function is 6 for x != 3, undefined for x = 3. However, in the limit of 6(x-3)/(x-3), we are in fact allowed to divide out (x - 3) by (x - 3). You are removing a hole in the graph but you should realize that holes don’t always mean the limit doesn’t exist. The limit is telling you what you can expect the graph to behave like at a certain point. It’s saying that if all neighbors around a point behave nicely, no matter how close the neighbors are, then we conclude the function has a limit at that point.
It is a simple case of noticing that the function is undefined at a point but its limit is not.
