The BEST explanation of Limits and Continuity!

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Uploaded by on Jul 7, 2010

Rohen Shah has been the head of Far From Standard Tutoring's Mathematics Department since 2006.Enjoy!

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Uploader Comments (FarFromStandard)

  • Thank u for the tutorial..

    But I'm confused at 3:50.

    Why is there no y value for x=3?

    From the way I see, there's one and it is y=4. How can it be not defined? Pls help to clarify..

  • @blakknwytt Excellent question! There is no y value for x = 3 because there is a hole. If instead it were a smooth curve, then you're right, the y value at 3 would equal 4. A "hole" literally means there is a gap on the function. So when x = 3, there is no y value at all. But when x = 2.99999, there is a y value, 3.99999 (so basically 4). And when x=3.00001, there is a y value, 4.00001 (basically 4). So the limit at x =3 is 4, but at x =3 there's no exact y value because there is a hole

  • Are piecewise functions always not limits? Or does it depend on which x value you approach?

  • @hameed That's a great question! Whether or not a limit exists ALWAYS depends on the x value - whether or not the function is piecewise. As the video says, for CONTINUOUS functions, the limit at any given x value will be = f(x). Piecewise functions can be continuous; the two that we happened to draw in this video were discontinuous, and so that's why the limits DONT exist ONLY at those specific x values. Limits existed on the continuous PARTS of those piecewise function. Hope that helps!

Top Comments

  • Hoooly crap. You're a LIFESAVER. How come I can understand you a lot better than the other tutors? XD

    I guess it's because you don't use a lot of mathematical vocabulary, and you use everyday words, which makes it easier to understand.

  • LOL on tags.

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All Comments (71)

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  • FUCK YOU CALCULUS AND TRIGNOMETRY!!!!!!!!!!

  • lol if i ever make a math tutorial video im gonna put "sexy hot murderer" in the tags so when people are searching "sexy hot murderer", my math tutorial on basic addition will come up (8

  • i PRETTY much got it XD good video.

  • you have nice marker hand writing

  • Thanks a lot! I had trouble visualizing limits and understanding exactly what they are but i think you pretty much cleared that up

  • This is "pretty much" and "clearly" well-explained :)

  • That was a great explanation! I feel I like I am starting to grasp the limit concept! Thanks so much!

  • Amazing. That is all that needs to be said. Great explanation with the first graph.

  • The explanation of lim( x->4 ) of f(x) with the diagram of a concave up parabola is inconsistent with what he was saying. It should be lim ( x->3 )of f(x) is 4.

  • I am very happy to see the vidoe from you, hopefully the others also are happy for You Rohen Shah has been the head of Far From Standard Tutoring's Mathematics Department since 2006.Enjoy

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