Essential Concepts
- The intuitive notion of a limit may be converted into a rigorous mathematical definition known as the epsilon-delta definition of the limit.
- The epsilon-delta definition may be used to prove statements about limits.
- The epsilon-delta definition of a limit may be used to find deltas algebraically.
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Glossary
- epsilon-delta definition of the limit
- [latex]\underset{x\to a}{\lim}f(x)=L[/latex] if for every [latex]\varepsilon >0[/latex], there exists a [latex]\delta >0[/latex] such that if [latex]0<|x-a|<\delta[/latex], then [latex]|f(x)-L|<\varepsilon [/latex]
- triangle inequality
- If [latex]a[/latex] and [latex]b[/latex] are any real numbers, then [latex]|a+b|\le |a|+|b|[/latex]