No, I understood it now. I was thinking the proof will be complete once we somehow prove delta is smaller than or equal to epsilon. I thought that in the last step you assumed |x-3| to be delta and somehow change the smaller than sign to smaller than and equals to. This what I had not got. But...
Does both \epsilon and ε represent epsilon? My textbook uses \epsilon (the "belongs to" / "is a member of") sign, but many use ε.
Shouldn't it be |f(x) - L| < \epsilon? You've written |f(x) - L| \geq \epsilon
What is "priori"?
How did you do the analysis?
Can you do the proof of this...
Then shouldn't x-a BE delta?
So then delta and epsilon are not related to each other. Is it? But the graphs I've seen suggest that they ARE related.And delta and epsilon are not related to each other means any can be bigger or smaller than other, right?
Thanks, I uinderstood it now.
The...
So if I pick epsilon=0.00001, what would delta be? Say lim_{x \rightarrow 2} (2x^2 + 3x - 14) = 0 . What would be delta? How do we find out? How are epsilon and delta related to each other? So delta is not smaller than or equal to epsilon?
This is how my book solves this question:
Find the limit...
Can I take epsilon = 600 billion as well?
And I remember my Calculus teacher mentioning that delta should be greater than or equal to epsilon. Why is this?
I still don't get it very nicely. I would appreciate if you could put it in simpler words.
The \epsilon - \delta definition of limit is given as follows:
I have some questions:
1. Can x be equal to a?
2. Is is that we can select \epsilon and \delta ourselves? How? Can any small number...
I'm studying limits now (for the first time) and though have understood the intuitive concept of limit, I didn't get at all the epsilon-delta concept.
What is epsilon and delta? What is x-2? I didn't get anything at all.
So please explain me these in detail.
Thanking you in advanced...
If |vector A + vector B| (magnitude of sum of vectors A and B) = |vector A + vector B| (magnitude of difference between vectors A and B), how can we show that theta is equal to pi/2?
I know that vector A - vector B can be equal to the sum of vectors A and B if vector B is a null vector, but...