why is the limit 2 .. as you can see at the point (2,2) the point is an open circle which mean this point isnt define. so why is the limit as x---2 =2?

Question

why is the limit 2 .. as you can see at the point (2,2) the point is an open circle which mean this point isnt define. so why is the limit  as x--->2 =2?

karim728 · Answer

attachment

holsteremission · Answer

Just because $f(x)$ isn't defined at $x=c$ doesn't mean $\lim\limits_{x\to c}f(x)$ doesn't exist.

When you're considering a limit, you're actually assuming that $x\neq c$, so you don't need to worry about the function's exact behavior AT $x=c$, but rather how it behaves AROUND $x=c$.

karim728 · Answer

ohh.. so then if i understand correctly f(2) will make it not defined then? right?

karim728 · Answer

not the lmit

johnweldon1993 · Answer

Correct, There is a discontinuity at f(2) but there is most definitely a limit as x approaches 2

karim728 · Answer

ok thanks guys