Calculus practice
L'Hopital's Rule worksheets
Evaluate indeterminate quotient limits with justified, repeated applications of L'Hopital's Rule.
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Confirm the indeterminate form before each use of L'Hopital's Rule, then give the exact limit, signed infinity, or DNE.
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The worked key records the original indeterminate form, differentiates numerator and denominator separately, and stops as soon as exact order or tail behavior settles the limit.
Learning objective
What this activity builds
Identify 0/0 or infinity/infinity, differentiate numerator and denominator separately, and resolve the exact terminal limit.
Worked example
What changes when L'Hopital's Rule applies?
Replace the quotient limit by the limit of f'(x)/g'(x).
Differentiate the numerator and denominator separately. Do not use the quotient rule.
Teaching notes
Make the practice count
- Write the indeterminate form before applying the rule.
- Check the form again before repeating the rule.
- Keep one-sided signs when a residual power remains.
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Choose the problem count and function families. Each key verifies the form and shows every justified application.