Formula

Tags

• Differential calculus
• Limit
• ε-δ definition

Detail

Explore the idea

Variables

• $x$Independent variable
• $a$Point or real constant
• $f$Function
• $\delta$Radius in the ε-δ definition
• $\varepsilon$Tolerance in the ε-δ definition
• $L$Limit value

Conditions

• $\Longleftrightarrow$
• $\forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilon$

Also known as

• epsilon-delta limit
• formal definition of limit

Related formulas

• Related

  Formula

  $$\lim_{x\to a}f(x)=L$$
  Open formulaOpen in section

• Related

  Formula

  $$\lim_{x\to a^-}f(x)=L_L,\qquad \lim_{x\to a^+}f(x)=L_R$$
  Open formulaOpen in section