posted by Calculus on .
can someone please explain
h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ? i d = 1 2 5 7 0 4 1 1 4 5
division by zero is NOT allowed
(x+5)/(x-3) is valid for all x except x=3
but I can evalute using limits...
Whatever you did using limits is wrong.
The limit at x=3 exists if lim x→3- equals lim x→3+.
In this case, the two are not equal, because they tend toward inifinity in opposite directions, so the limit does NOT exist. Even if they tend toward infinity in the same direction, the limit does not exist.
Even in the case where the limit exists, as in the case of
the point x=3 remains a hole in the domain of f(x).
In the case of f(x)=(x+5)/(x-3), there is no doubt that the point x=3 is excluded from the domain, which is ℝ\3.