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Section 2.1 L’Hopital’s Rule
Subsection 2.1.1 L’Hopital’s Rule Summary
Determine if the limit is an indeterminate form, and if so, then what form it is.
If it’s
\(\frac{0}{0}\) or
\(\frac{\infty}{\infty}\text{,}\) then apply L’Hopital’s rule directly.
If it’s
\(0 \cdot \infty\) (or
\(\infty \cdot 0\) ), flip one of the terms to convert it to
\(\frac{0}{0}\) or
\(\frac{\infty}{\infty}\) (whichever is more convenient).
If it’s
\(\infty - \infty\text{,}\) then write it as one fraction first, and then continue.
If it’s an indeterminate form with an exponent, like
\(1^{\infty}\text{,}\) \(0^0\text{,}\) or
\(\infty^0\text{,}\) then first use logarithms.
