Examples of Continuity

Calculus: Find all points where the function is continuous. If a discontinuity is removable, find the best fitting point.

[MathDoctorBob]

@MultiMoe91 You're welcome!

If we divide by zero, the function is not defined at the point, so it is not continuous at the point. If we have 0/0, it is still discontinuous. There is a chance that the limit exists, in which case we have a removable discontinuity. That just means we can "fix" the graph by filling in the hole. - Bob

[Pv]

thank you so much you made it much clearer for me, excellent video

[MathDoctorBob]

@igetdoughboy420 - They are not in the domain of the function. The definition of continuity at a point x requires three things: 1) that f is defined at x (a fails this), 2) that the limit of f at x exists, and 3) that the limit equals f(x). (See video Continuity 1a.)

For a rational function, the discontinuities are the points where the denominator equals zero. (See video Continuity 1b - right before this one in the playlist.)

[MathDoctorBob]

@JRLOC488 You're welcome. Thanks for the comment. -Bob

[MathDoctorBob]

Great! Continuity can take a while to click.

[chelseyalise]

On the second example, when you plugged two into the function, the answer is 0/0 not 0/-1 because (2-2)(2-3) is 0. Your answer is still 0 though, which is correct.

[MathDoctorBob]

I'm assuming we cancel some (x-2) factors. I actually say this, pointing to the simplified function (x-2)/(x-3), x not 2, up top, then to 0/-1.

[MultiMoe]

thanks for the videos Dr.
i wanted to make sure... you said its continues everywhere except with makes the denominator = 0?
what if that value makes the numerator = 0 also?
will that be considerd as a point of dicontiniuty?
thanks :)