- #1

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I would like to learn how I can use the formal definition of a limit to prove that a limit does not exist. Unfortunately, my textbook (by Salas) does not offer any worked examples involving the following type of limit so I am not sure what to do. I write below that delta = 1 would seem to work because f(x) = 1/x increases without bounds on (0,1].

Thank you for your help.

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## Homework Statement

[tex] \begin{align}

& \text{Prove that }\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}\text{ does not exist}\text{.}

\end{align}[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]>\begin{align}

& \text{I know that I must negate the limit definition, as such:} \\

& \forall \text{L,}\exists \varepsilon \text{0 st }\delta \text{0, }\left| x-c \right|<\delta \Rightarrow \left| f(x)-L \right|\ge \varepsilon \\

& \text{Also, I believe that if I take }\delta =1,\text{ this value will help me with the above}\text{.} \\

& \text{However, how would I go about doing this? }

\end{align}[/tex]