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Interactive video lesson plan for: Jump discontinuities - What are they?

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► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course

In this video we’re talking about jump discontinuities, or discontinuities of the first kind. These kinds of discontinuities are big breaks in the graph, but not breaks at vertical asymptotes (those are specifically called infinite/essential discontinuities). You’ll often see jump discontinuities in piecewise-defined functions. A function is never continuous at a jump discontinuity, and it’s never differentiable there, either.

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0:18 // What are jump discontinuities? What are they compared to infinite/essential discontinuities?
0:52 // The general limit will never exist at a jump discontinuity
1:59 // What’s going on at x=-2?
4:46 // What’s going on at x=3?
7:05 // What’s going on at x=5?
8:22 // How to find the value of the function at a jump discontinuity

When you’re looking at the behavior of a function at a jump discontinuity, you already know that the general limit doesn’t exist, that the function isn’t continuous, and also that it’s not differentiable. Which means that all you really have left to investigate are the one-sided limits, and the actual value of the function at that point.

The one-sided limits will never be equal if it’s a jump discontinuity, so you want to look at the left-hand limit by tracing the function from the left, or negative side, and identifying the y-value where you run out of graph. You also want to trace the function from the right, or positive side, and identify the y-value where you run out of graph. This will give you the left- and right-hand limits, respectively.

You'll also want to see where the graph has a "filled in" circle. It might be connected to the left piece of the graph, or to the right piece of the graph, or it might be floating somewhere else along the vertical line where the jump discontinuity exists. Regardless of where it is, the filled in circle represents the function's actual value at that point.

Music by Joakim Karud: http://soundcloud.com/joakimkarud

● ● ● GET EXTRA HELP ● ● ●

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● ● ● CONNECT WITH KRISTA ● ● ●

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?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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Tagged under: find jump discontinuities, jump discontinuities,jump discontinuity,jump discontinuities,discontinuity kind,break discontinuity,discontinuities,-sided limits,left-hand limit,-hand limit, function,limits,calculus

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