► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course
The general limit of a function at x=a is the value the function approaches as x gets very close to "a" from either side of "a".
Similarly, the right-hand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the right-hand side (or positive side) of "a". And the left-hand limit at x=a is the value the function approaches as x gets very close to "a" as you move in from the left-hand side (or negative side) of "a".
It's these left- and right-hand limits that we call one-sided limits, and it's important to understand how to calculate one-sided limits because they're part of the definition of the general limit.
In order for the general limit of a function to exist at x=a, the left-hand limit must exist at x=a, the right-hand limit must exist at x=a, and the value of the left- and right-hand limits must be equal to each other. If all three of these conditions are met, then we can say that the general limit exists at x=a. Otherwise, if any one or more of the conditions are not met, the general limit cannot exist at x=a. If the general limit does not exist, it implies that there's a discontinuity in the graph at that point.
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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?!”
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: ,calculus,-sided,limits,limits continuity,Krista King, hand limit,left hand limit,educational,general limit,expert
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