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junior college 2 | H3 Maths
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pls help
Date Posted: 5 years ago
Views: 491
https://brilliant.org/wiki/epsilon-delta-definition-of-a-limit/
I'm not sure how to prove the limit of a constant function
nvm I got it alr!
let f(x) = c
0 < |x - a| < δ ⇒ |f(x) - c| < ε
So |c - c| < ε
|0| < ε → 0 < ε
So 0 < ε no matter which δ you choose.
0 < |x - a| < δ ⇒ |f(x) - c| < ε
So |c - c| < ε
|0| < ε → 0 < ε
So 0 < ε no matter which δ you choose.
I've added an answer to this but am not sure if the way I proved is correct, can you help me see?
I'll take a look
See 1 Answer
done
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can I prove like that?
Date Posted:
5 years ago
δ has to be a constant, it can't have the x inside it
oh I see, then how do I manipulate such that a constant is formed?
https://math.stackexchange.com/questions/1312410/proving-a-limit-of-a-constant-function
You can just let δ = a positive number which is ≤ ε . No matter which δ you choose here, ε always > 0. So |c - c| always < ε
The proof for the limit of a constant function is done differently from the usual
You can just let δ = a positive number which is ≤ ε . No matter which δ you choose here, ε always > 0. So |c - c| always < ε
The proof for the limit of a constant function is done differently from the usual
https://en.m.wikibooks.org/wiki/Calculus/Proofs_of_Some_Basic_Limit_Rules
It is that simple
It is that simple
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