3 cases for a function to be discontinuous

Let's talk about the 3 cases for a function to be discontinuous. The 3 types of discontinuity are vertical asymptote, removable discontinuity, and jump. This topic is usually covered at the beginning of calculus 1 or precalculus. For more calculus tutorials, subscribe to @bprpcalculusbasics

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[Ninja]

I wonder, is it possible to have a function to have a jump without using piecewise? That would be very interesting.

[JoachimFavre]

There is also an important one, which is oscillation. For example, the function sin(1/x) if x != 0 and 0 if x = 0 is not continuous at 0. This is really important, because it allows us to find a function which derivative is not continuous. x^2 sin(1/x) if x != 0 and 0 if x = 0 is differentiable at 0 (you can do it using the definition of the derivative, it gives 0), but its derivative is not continuous at 0 since the lim x->0 f'(x) does not exist (it oscillates) :D

[iAzazelHD]

Well, some people say f(x) = 1/x is continous, since 0 doesnt belong to the domain so it makes no sense saying it is discontinous on a point where the function is undefined.

[kobethebeefinmathworld]

me: RD - Rational Denominator? Real Domain?
blackpenredpen: RD - Removable Discontinuity
me: 😂

[flaviuzzz]

Thank you, my teacher mentioned discontinuous functions last week, can't wait to see the special cases.
Love what you do man

[Rainer]

I love your content, your really good at explaining this. I’m only in algebra 2 so I haven’t even started precalc but the way you explain it makes sense

[zahidiqbal]

I was really looking for this content.
Thank u sir 😘

[yoav]

Nice! I think you should change the third to S.M (super mario) discont.

[teelo]

> I don't think Super Mario can do that
Challenge Accepted.

[vitalsbat]

hi bprp do you have a way to remember the sum/product of trigo functions? i am so confused fight now idk which is x2 and x0.5

[ДенисКосько-ни]

2:37 thought the 2nd example was gonna be sin(x)/x

[Harry-fwhv]

Can a function be discont. by oscillation?

[kepler]

ohhh, and I thought I will be getting epsilon deltas for discontinuous functions

[jagdishsolanki]

Sir why
arcsin(sinx) = x
arctan(tanx) = x
Etc.
Please make video on this topic 🙏🏻