8 февр. 2018 г. · @Jwan622 It basically means that limx→af(g(x))=f(limx→ag(x)) if f is continuous at limx→ag(x). So the lim and f can "switch places". And the ≡ ...

15 июл. 2016 г. · limn→∞(1+1n)n is a definition of e as it models n moments of growth occurring where at each instant the initial value is scaled by a factor limn ...

22 авг. 2021 г. · I tried to follow the answer of this post, but there is something I don't understand: Prove ex limit definition from limit definition of e.

27 июн. 2015 г. · This is probably the most complicated definition of ex and it needs substantial work to prove many properties of ex.

5 февр. 2018 г. · I occasionally see proofs where the limit definition for e pops up and I don't recognize it for some reason, every time! e=limn→∞(1+1n)n.

22 июн. 2015 г. · How the fact that the double limit limn→∞k→∞an+1,k+1an,k is smaller than 1 (if it exists) is helpful for this? Next, f(n) is strictly increasing ...

1 мар. 2019 г. · For fun, I tried to prove the well-known exponential property ea+b=eaeb using the limit definition of the exponential function, below.

19 авг. 2014 г. · "Indeed in high-school 'e' was defined as the limit of this particular sequence. However none of us could come up with a 'rigrous' proof that ...

6 июн. 2017 г. · Therefore, limh→0ah−1h exists. Now we are ready to prove that there exists an e such that limh→0eh−1h=1. Define e=a1k, where k=limh→0ah−1 ...

3 апр. 2020 г. · Proof that exponential function's limit definition increases monotonically? ... It is well known that we can define ex by the following limit. ex= ...