Calculus I (MATH 101) L'H??pital's Rule Practice Problems (Indeterminate Forms, Limits, Exponentials)
Massachusetts Institute of Technology
Calculus I (MATH 101) | Practice Problems

Overview
A Calculus I practice set for the end-of-term limits unit: identify indeterminate forms, rewrite before differentiating, and apply L'H??pital's rule only when it is valid.

Key topics
•indeterminate forms (0/0, ???/???, 0?????, ???-???, 0^0, 1^???, ???^0)
•rewriting tricks (common denominators, factoring, conjugates)
•log transforms for exponential forms
•limits at infinity and dominant growth
•when L'H??pital's rule is not allowed

Suggested study tasks
•classify 20 limits by form and choose a rewrite strategy
•solve 15 L'H??pital limits (show the justification each time)
•convert 10 power/exponential limits using ln then exponentiate
•do 8 dominant-growth comparisons (polynomial vs log vs exponential)
•write a one-page decision checklist for when to use L'H??pital

Common pitfalls
•using L'H??pital without confirming 0/0 or ???/???
•differentiating before simplifying algebraic cancellations
•forgetting to rewrite ???-??? forms first
•dropping absolute values in ln transforms
•losing track of domain restrictions