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Indeterminate Forms and L’Hopital’s Rule

Indeterminate Forms and L’Hopital’s Rule. Lesson 8.7. Problem. There are times when we need to evaluate functions which are rational At a specific point it may evaluate to an indeterminate form. Example of the Problem. Consider the following limit: We end up with the indeterminate form

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Indeterminate Forms and L’Hopital’s Rule

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  1. Indeterminate Forms and L’Hopital’s Rule Lesson 8.7

  2. Problem • There are times when we need to evaluate functions which are rational • At a specific point it may evaluate to an indeterminate form

  3. Example of the Problem • Consider the following limit: • We end up with the indeterminate form • Note why this is indeterminate

  4. L’Hopital’s Rule • When gives an indeterminate form (and the limit exists) • It is possible to find a limit by • Note: this only works when the original limit gives an indeterminate form

  5. Example • ConsiderAs it stands this could be • Must change to format • So we manipulate algebraically and proceed

  6. This is not an indeterminate result Example • Consider • Why is this not a candidate for l’Hospital’s rule?

  7. Example • Try • When we apply l’Hospital’s rule we get • We must apply the rule a second time

  8. Hints • Manipulate the expression until you get one of the forms • Express the function as a fraction to get

  9. Assignment • Lesson 8.7 • Page 574 • Exercises 1 – 33 EOO

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