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AP Calculus AB 4.7 L’Hospital’s Rule Question Bank

Practise indeterminate-limit questions by checking the form and applying L’Hospital’s Rule when its conditions are met.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • recognise indeterminate forms and verify when L’Hospital’s Rule applies
  • evaluate the resulting limit and justify the selected method

LIM-4.A—Determine limits of functions that result in indeterminate forms question 1

[Maximum number: 1]

The functions f(x), g(x), and h(x) have derivatives of all orders. Listed above are values for the functions and their first and second derivatives at x=3. Find lim⁡x→3(f(x))2−3h(x)g(x)+h(x)\lim _{x \rightarrow 3} \frac{(f(x))^{2}-3 h(x)}{g(x)+h(x)}.

A

−15-\frac{1}{5}

B

12\frac{1}{2}

C

1

D

nonexistent

Figure for Question LIM-4.A—Determine limits of functions that result in indeterminate forms question 1 — AP Calculus AB
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