Home/Differential Calculus/Infinite limits/Formula2.7. Infinite limitsFormulaIn 2.7. Infinite limitsFormulaCopy LaTeXlimx→af(x)=+∞⟺∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)>M\lim_{x\to a}f(x)=+\infty \quad\Longleftrightarrow\quad \forall M>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow f(x)>Mx→alimf(x)=+∞⟺∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)>MTagsDifferential calculusLimitInfinite limitsVariablesxxxIndependent variableaaaPoint or real constantfffFunctionδ\deltaδRadius in the ε-δ definitionConditions⟺\Longleftrightarrow⟺∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)>M\forall M>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow f(x)>M∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)>MFound an error? Contact us.Related formulasRelatedFormulalimx→af(x)=−∞⟺∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)<−M\lim_{x\to a}f(x)=-\infty \quad\Longleftrightarrow\quad \forall M>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow f(x)<-Mx→alimf(x)=−∞⟺∀M>0 ∃δ>0: 0<∣x−a∣<δ⇒f(x)<−MOpen formulaOpen in section