Home/Differential Calculus/Notation, functions and domains/Intervals and absolute valueSection 1.1Intervals and absolute valueFormulaCopy LaTeX∣x∣={x,x≥0−x,x<0|x|=\begin{cases} x, & x\ge0\\ -x, & x<0 \end{cases}∣x∣={x,−x,x≥0x<0Piecewise definition of absolute value.View detail →FormulaCopy LaTeX∣x−a∣<δ⟺a−δ<x<a+δ|x-a|<\delta \quad\Longleftrightarrow\quad a-\delta<x<a+\delta∣x−a∣<δ⟺a−δ<x<a+δSymmetric neighborhood of radius δ\deltaδ around aaa.⟺\Longleftrightarrow⟺a−δ<x<a+δa-\delta<x<a+\deltaa−δ<x<a+δView detail →FormulaCopy LaTeXx2=∣x∣\sqrt{x^2}=|x|x2=∣x∣View detail →
FormulaCopy LaTeX∣x∣={x,x≥0−x,x<0|x|=\begin{cases} x, & x\ge0\\ -x, & x<0 \end{cases}∣x∣={x,−x,x≥0x<0Piecewise definition of absolute value.View detail →
FormulaCopy LaTeX∣x−a∣<δ⟺a−δ<x<a+δ|x-a|<\delta \quad\Longleftrightarrow\quad a-\delta<x<a+\delta∣x−a∣<δ⟺a−δ<x<a+δSymmetric neighborhood of radius δ\deltaδ around aaa.⟺\Longleftrightarrow⟺a−δ<x<a+δa-\delta<x<a+\deltaa−δ<x<a+δView detail →