Epsilon Delta Definition of a Limit

This video explains the Epsilon Delta Definition of a Limit. Then 1 example is worked out where Delta is found when given the Limit and a value for Epsilon.

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[dis_guy]

after like 6 videos now this is the best explanation

[FreshBeatles]

THANK YOU VERY HELPFUL THIS WAS THROWN AT US FOR OUR FIRST LESSON CALC 1 THANKS

[kingbeauregard]

The way that makes it click for me is, imagine a rectangle centered at (a, L) that is tall enough that the function never touches the top or bottom of the rectangle. Can you shrink that rectangle down to nothing, such that there is no size where the function touches the top or bottom edge? The dimensions of the rectangles are described by a relationship between epsilon and delta: the height is 2*epsilon, the width is 2*delta. Very often the relationship between the two is linear, so that the rectangle never changes shape as you resize it; but it's okay for the relationship to be non-linear, just so long as an epsilon of zero means a delta of zero.

In terms of the technique, I find the practical thing is to look at | f(x) - f(a) | and try to find some way to mingle the f(x) and f(a) such that a term of "x-a" emerges. Then your job is to find a way to isolate that "x-a", and then get rid of any remaining x's by replacing them with something that makes the | f(x) - f(a) | uniformly larger (or at least the same size). At that point, we're switching to doing epsilon-delta on a different function, but then we're doing squeeze proof logic: if that different function has a limit of L at x=a, and that different function is always "bigger" than the original function, then the original function must have that same limit.

[vinodreddy]

It's a good explanation, can you make a video on epsilon-delta method it would be helpful ...!!!