AP®MathsCollege BoardCalculus ABExam QuestionsUnit 4: Contextual Applications of DifferentiationL'Hospital's Rule

L'Hospital's Rule (College Board AP® Calculus AB)

Exam Questions

18 mins10 questions

Select a question set to download for
L'Hospital's Rule

Select an answer set to view for
L'Hospital's Rule

1
Sme Calculator1 mark

limit as x rightwards arrow 4 of fraction numerator x cubed minus 64 over denominator x minus 4 end fraction equals

  • 0

  • infinity

  • 48

  • 12

Choose your answer

Did this page help you?

2
Sme Calculator1 mark

If a not equal to 0, then limit as x rightwards arrow a of fraction numerator x squared minus a squared over denominator x to the power of 5 minus a to the power of 5 end fraction is

  • nonexistent

  • 0

  • fraction numerator 2 over denominator 5 a cubed end fraction

  • fraction numerator 3 over denominator 7 a cubed end fraction

Choose your answer

Did this page help you?

3
Sme Calculator1 mark

If f to the power of apostrophe open parentheses x close parentheses equals sin x minus 1 and g to the power of apostrophe open parentheses x close parentheses equals 2 for all x, and if f open parentheses 0 close parentheses equals g open parentheses 0 close parentheses equals 0, then limit as x rightwards arrow 0 of fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction is

  • nonexistent

  • negative 1 half

  • 0

  • 1 half

Choose your answer

Did this page help you?

4
Sme Calculator1 mark

limit as x rightwards arrow fraction numerator 3 pi over denominator 2 end fraction space of fraction numerator sin space x plus 1 over denominator cos space x end fraction equals

  • 0

  • infinity

  • 1

  • nonexistent

Choose your answer

Did this page help you?

5
Sme Calculator1 mark

limit as x rightwards arrow 0 of fraction numerator 1 minus cos squared open parentheses 3 x close parentheses over denominator open parentheses 3 x close parentheses squared end fraction equals

  • 0

  • 1 third

  • 1 over 9

  • 1

Choose your answer

Did this page help you?