> [!summary] Indeterminate products are in the form $0\cdot \infty$. To solve indeterminate limits, the limit is rewritten as a quotient of two products. Converting into another indeterminate form, which can be resolved. >[!info]+ Read Time **⏱ 1 min** # Definition Indeterminate products are [[Limits|limits]] that result in the form $0 \cdot \infty$, an [[Indeterminate Forms|indeterminate form]]. To solve these issues, the limit is written as two products $fg$ and rewritten as a quotient, $ fg=\frac{f}{\frac{1}{g}} \space \text{ or } \space fg=\frac{g}{\frac{1}{f}} $ This rewrites the limits in another indeterminate form, $\frac{0}{0}$ or $\frac{\infty}{\infty}$. Then the limits is algebraically manipulated by [[Multiplying by the Conjugate|multiplying by the conjugate]] or [[L'Hôpital's Rule|L'Hospital's Rule]] to evaluate the limits. > [!note]- Why can $fg$ be written as $\frac{f}{\frac{1}{g}}$ or $\frac{g}{\frac{1}{f}}$? Since $fg=\frac{f}{\frac{1}{g}}$ and $fg=\frac{f}{\frac{1}{g}}$, you are not changing the limit itself since you can always reduce back into $fg$. Which is mathematically allowed. > [!note]- How do I know which product to flip? There is no algorithm of which to flip and which to keep. One will work, and one wont. There are patterns though.