L'Hopital's Rule
Read this section to learn how to use and apply L'Hopital's Rule. Work through practice problems 1-3.
Practice Answers
Practice 1:
(a) . The numerator and denominator are both differentiable and both equal when , so we can apply l'Hô pital's Rule:
(b) . The numerator and denominator are both differentiable functions and they both equal when , so we can apply l'Hô pital's Rule:
Practice 2: . The numerator and denominator are both differentiable and both become arbitrarily large as becomes large, so we can apply l'Hô pital's Rule:
" ". Using l'Hô pital's Rule again:
Practice 3: Comparing with operations to with operations. " " so use L'Hopital's Rule: so requires fewer operations than .
Comparing with operations to with operations.
so requires fewer operations than . requires the fewest operations of the three algorithms.
Comparing with operations to with operations. Using l'Hô pital's Rule several times:
so requires more operations than . requires the most operations of the three algorithms.