(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if [itex]L \neq 1 [/itex], the statement [tex] \lim \limits_{x \to \infty} (1+\frac{1}{x}) = L [/tex] is false.

2. Relevant equations

The Definition of a Limit

3. The attempt at a solution

So I've been trying to prove this by negating the logical statement of the definition of a limit; i.e. by trying to prove that

[itex]\exists \epsilon > 0 [/itex] such that [itex]\forall \delta >0 \exists x > \delta [/itex] such that [itex]\left|f(x)-L\right|\geq \epsilon[/itex].

I know that when [itex]L=1[/itex] the limit exists; that is no trouble to prove. The problem is that every time i try to find an x that works, I can never make it work in my proof. Am I going about this the right way?

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# Homework Help: Proving a limit is false when L does not equal 1

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