Yes, it means exactly that. The limit does not exist.
BTW
[tex] \displaystyle\lim _{x \to 2} \frac{{x^2 - 2x + 6}}{{x - 2}}[/tex] gives .
Hey!
I encountered a question in my homework that was: "Evaluate the limit, if it exists".
It is not possible to factor out the denominator of this equation. I tried dividing (x-2) into the equation and got a solution of x+1R8.
My question is: if I can't factor out the denominator of a rational equation, and the limit is asking where that equation would have the denominator at 0 (in the example 2) does this mean the limit does not exist?
I hope I made sense in my question.
Thanks!
Since you titled this "general question", here is a "general" answer.
To find the limit , first try just putting x= a. If Q(a) is not 0, the limit is just (even if P(x)= 0). If Q(a)= 0 but P(a) is NOT 0, then the limit does not exist. If both P(a) and Q(a) are 0, then both P(a) and Q(a) must have a factor of x- a which can be cancelled.