Home/Differential Calculus/Graphs and asymptotic behavior/Horizontal asymptotesSection 15.2Horizontal asymptotesFormulaCopy LaTeXy=L is a horizontal asymptote⇔limx→+∞f(x)=L or limx→−∞f(x)=Ly=L\text{ is a horizontal asymptote} \Leftrightarrow \lim_{x\to+\infty}f(x)=L\ \text{or}\ \lim_{x\to-\infty}f(x)=Ly=L is a horizontal asymptote⇔x→+∞limf(x)=L or x→−∞limf(x)=LMay exist only as x→+∞x\to+\inftyx→+∞ or x→−∞x\to-\inftyx→−∞; both are not required simultaneously.View detail →
FormulaCopy LaTeXy=L is a horizontal asymptote⇔limx→+∞f(x)=L or limx→−∞f(x)=Ly=L\text{ is a horizontal asymptote} \Leftrightarrow \lim_{x\to+\infty}f(x)=L\ \text{or}\ \lim_{x\to-\infty}f(x)=Ly=L is a horizontal asymptote⇔x→+∞limf(x)=L or x→−∞limf(x)=LMay exist only as x→+∞x\to+\inftyx→+∞ or x→−∞x\to-\inftyx→−∞; both are not required simultaneously.View detail →