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### Course: Calculus, all content (2017 edition)>Unit 1

Lesson 3: Limits from graphs

# Limits from graphs: limit isn't equal to the function's value

Sal finds the limit of a function given its graph. The function's value at the limit is different from the limit's value, but that doesn't mean the limit doesn't exist!

## Want to join the conversation?

• What if the point of discontinuity falls on the function? Does that mean it fills a hole or did it just happen to fall there?
• If that were the case then it wouldn't be a point of discontinuity. It would simply be a continuous function.
• At Sal talks of "g of negative 6.999." Does he mean to say "negative?" Isn't the 6.999 positive?
• He said "g of negative 6.999" but it should be "g of 6.999". I'm guessing what he was trying to say that g of 6.999 is still negative but got mixed up. Report it so he can add an annotation for correction.
• I don't understand the point here? You have graphed an undefined function then picked a random point off the line and are showing that it is off the line... ok

It would be very helpful here to give us the function that plots out to the graph shown yet is discontinuous at X=7
• He made it much easier for us by showing us only the line. It is much simpler and easier to understand than if he actually defined the function.
• Would it be possible to actually write up a function for this graph with the discontinuity, or is it purely hypothetical?
• You can define such a function as a "piecewise continuous" function. For certain parts of the graph, it'll act like one function, but on other parts, it'll act in a completely different way.
• Is the following statement correct: The function approaching 7 is zero, however, the function at 7 is 3. Thanks for any feedback!
• what is the function g(x) defined as?
• He does not define the function, as far as I could see.
• Why the function's actual value g(7) is not greater than 9?
(1 vote)
• The little blue dot that is disconnected from the curve is where g(7) is defined, which as a value of 3, which is less than 9.
• But in all the previous cases we sae that the limit was approaching infinity but the value of limit wasnt infinity ... So is there discontinuity present too?
• Are we supposed to be already aware of what "Continuity" is; before we begin learning this (Calculus) subject?! ^_^
(1 vote)
• It is possible to learn how to compute integrals and derivatives without understanding continuity.

But if you really want to understand what calculus is, you'll start with some basic notions like continuity (or even more basic things like limits of sequences). You can then build up from there, so even when you get to more advanced parts of calculus, you can still understand it in terms of these basic notions.
• Is it possible to figure out the limit of functions without tables or graphs??
(1 vote)
• Yes e.g.1:

y = x (linear function, continuous)
thus the limit of any point can be obtained by subbing in the x value into the equation.

The other two ways are factoring and multiply by the conjugate, if you have time, check out this video: