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Section 5.5 L’Hôpital’s rule
Objectives
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Use L’Hôpital’s Rule to evaluate limits where numerator and denominator both approach zero or infinity.
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Interpret limits in terms of relative growth rates.
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Use algebraic or logarithmic rewrites to handle other indeterminate forms.
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If \(\limit{x\to a}f(x)=\limit{x\to a}g(x)=0\text{,}\) then
\begin{equation*}
\limit{x\to a}\frac{f(x)}{g(x)}=\limit{x\to a}\frac{f'(x)}{g'(x)}
\end{equation*}
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Same goes for if
\(f\) and
\(g\) are both approaching infinity
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For other indeterminate forms, use algebraic massage or logarithms
