Transcription of Further Examples of Epsilon-Delta Proof
{{id}} {{{paragraph}}}
Example: confidence
Further Examples of Epsilon-Delta Proof
Further Examples of Epsilon-Delta ProofYosen Lin, 16, 2001 The limit is formally defined as follows:limx af(x) =Lif for every number >0 there is a corresponding number >0 such that0<|x a|< = |f(x) L|< Intuitively, this means that for any , you can find a such that|f(x) L|< .To do the formal Proof , we will first take as given, and substituteinto the|f(x) L|< part of the definition. Then we will try to manipulatethis expression into the form|x a|<something. We will then let be this something and then using that , prove that the condition holds. Someexamples should make this Prove:limx 4x= 4We must first determine whataandLare.
=) j(3x 1) 2j< =) jf(x) Lj< This completes the proof. 3. Prove: lim x!1 p x= 1 In this problem, we have a= 1and L= 1. If we try to apply the proof directly, we will end up jf(x) 1j < , which produces a meaningless result, since, anything minus 1is 1. Therefore, we need to modify or de nition of limit slightly for in nity problems.
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: