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I literally didn't understand anything my college professor was talking about during class. What she failed to elaborate in one and a half hour, you explained brilliantly in seven minutes. Kudos!
I AM a morrocan student ! still in college and we learned this lesson !! ALL I WANNA SAY IS THANK YOU SO MUCH BECAUSE IT SIMPLIFIED EVRYTHING AND IT CLARIFIED WHAT I DID NOT UNDERSTAND IN CLASS !! THANK YOU SO MUCH !
I know it's late to comment, but it may help someone, he means is epsilon of L or 0.01 of L because limit boundaries that we are defining that is epsilon+L and epsilon-L are very small so you can say epsilon is very small or 0.0001 or anything.
for the first time in a year this actually makes sense. Ive gone all the way to cal 3 and diff eq, never needed this for those classes other than cal 1 but its just one of those things thats always mystified me ever since i saw it, until now
There are two ways of writing epsilon in mathematics; one way is to write it like Sal did, and the other is as you're describing. In LaTeX (math mode), they would be \epsilon and \varepsilon, respectively.
Sal, I think it would help with the intuition if you bring in some topology concept, such as the open ball (of course don't have to define it rigorously but I think the open ball concept can help first time learners with epsilon-delta). And it does expose students to functions of higher dimensions. "Given epsilon > 0, we can find a delta such that for a point [z] living in the space of radius delta in the domain, the image of z [aka f(z)] will be within a space of radius epsilon in the range."
Thanks! Is the idea behind using this for limits to see whether one’s graph stays continuous and within the box? If it is discontinuous on L, then, for small €, D would not be able to be anything but zero, defying your concrete shape. If is is smooth, then a nonzero D may be chosen, always.
If it wasnt for you i wouldn't even have cleared my tenth grade.... Thank you so much...... Once i become rich I'll help you in every single possible way i can :D
I've watched a bunch of videos about the topic and it's crystal clear to me that if the limit of f(x) is within epsilon of L, then x is within delta of a. I can visualize it, express it mathematically and it makes perfect sense, however, how does that prove a limit???
so what would happen if (x-c) was equal to or greater than delta? or likewise for (f(x)-L) equal to or greater than epsilon? I don't understand exactly how the absolute value part factors in
Does this definition apply to sequences too? if so explain how please And if not do you know where I can find a video that explains the definition of limits of sequences?
Yoshis Vids This definition applies everywhere one uses the concept of limits, and of course also sequences. Please elaborate more specifically about what you're looking for so that I can help further, in case it's still not clear. :)
can i take any value of epsilon and delta, i mean be it of range 2 or 3 units or it must be very small. if it can be large as 2 or 3, does this defination holds for exponential functions?
Your definition is wrong! Should be within delta of c, BUT NOT EQUAL TO C, then f(x) will be within epsilon of L. Without the "BUT NOT EQUAL TO C" clause you get the wrong answer when there is a discontinuity at c!
I believe Paul means that there should be a ' > 0 ' part on the |x - c|, to ensure x is not equal to c. So the definition as written is technically incorrect, albeit a very minor issue.
Sal, I think it would help with the intuition if you bring in some topology concept, such as the open ball (of course don't have to define it rigorously but I think the open ball concept can help first time learners with epsilon-delta). And it does expose students to functions of higher dimensions. "Given epsilon > 0, we can find a delta such that for a point [z] living in the space of radius delta in the domain, the image of z [aka f(z)] will be within a space of radius epsilon in the range."
