How to find REMOVABLE DISCONTINUITIES (KristaKingMath)

Discontinuities can be characterized as either removable or nonremovable. Removable discontinuities are also called point discontinuities, because they are small holes in the graph of a function at just a single point. They are called removable because they can be "removed" just by redefining the function as the limit of the function at that particular point.

In contrast, nonremovable discontinuities are big breaks in the graph, like asymptotes. They can't just be "filled in" by redefining the function at a point, thereby making it continuous. Therefore, they can't be removed.

You'll usually find removable discontinuities in rational functions, and the removable discontinuity can usually be identified by factoring the numerator and denominator of the function and canceling like factors. It's the solution of these canceled factors that indicate the removable discontinuity.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[keekli]

Any videos about discontinuity did not go into this much detail about removable ones. So cool that this one does explain in full detail.

[firebird]

Wow. You just made me understand this so much better than anything I’ve done to this point.

[deborahcaleb]

Amazing. So simple and concise, explained everything so well, perfect for studying for finals!

[yongseo]

this seriously helped me! Thank you so much!

[thebluebeyond]

I'm Saved again! by this channel 😭❤️❤️❤️❤️

[haleyanderson]

how do you know if there are no nonremovable discontinuities? One of my test questions was this expression flipped and there were no nonremovable discontinuities

[流輪]

beautiful voice with clear explaination

[gurwinderkaur]

Pls make a video how to find removable discontinuity of a function with two variable

[sangachidam]

Very good explanation. Thank you very much

[Ana-cthi]

Then, how to clasify this function
X^4 / x^4-1 ?

[josecasillas]

Ok, but are the original function and the simplified function equivalent? One is indeed a simplified version of the other, so I would assume that a removable discontinuity simply includes you defining the function f as the original function you had, we'll call it f(x), everywhere except a c, and then define the same function f as, say g(x), only at c, so as to make f continuous everywhere, including c. So are g(x) and f(x) equivalent? I mean f(x) doesn't give you 1/4, but its simplified version does. Yet, if you graph them, they both produce the IDENTICAL graphs. So how is one discontinuous at c (in this case 2) and the other isn't? That's what I don't understand. My guess is that f(x) = g(x), only that g(x) is defined in such a way that the function is not discontinuous at 2, so by calculating g(2), you can apply that functional value to f(x), since f(x) = g(x). Then you'd have a piece-wise where F(x)= f(x) at every real value of x and g(x) when x = c? Is that basically what it is?

[orderrr]

your definition for discontinuity is a little bit vague you said "a discontinuity is found wherever theres an undefined point.( Im assuming you mean an infinity?)" but with a counterexample (sinx / x) I can show you that your point isn't generally true.
Otherwise, I really like your work. Cheers.

[ijustwantvibee]

calculus from youtube is better than college