L'Hopital's Rule Worksheet with Answer Key

What's on the worksheet

1. Evaluate each limit with L'Hopital's rule.
   \displaystyle \lim_{x \to 2} \dfrac{e^{x - 2} - 1}{x^3 - 8}\displaystyle \lim_{x \to 9} \dfrac{\sqrt{x} - 3}{\ln(x - 8)}\displaystyle \lim_{x \to 1} \dfrac{2^x - 2}{x^2 - 1}\displaystyle \lim_{x \to 0^+} \dfrac{\ln(\sin x)}{\ln x}
2. Use L'Hopital's rule to evaluate the limit, checking its hypotheses first.
3. Each limit needs L'Hopital's rule more than once.
4. Name the indeterminate form, rewrite it as a quotient, and evaluate.
5. Name the indeterminate form, take logarithms, and evaluate.
6. Ben models his sled on a snowy hill with air drag.
7. Liam works on _x 1 x + 1(x - 1)².