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AP Calculus AB Derivative Limit Definition Question Bank

Practise AP Calculus AB derivative questions by interpreting difference quotients and limits as derivative definitions.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • interpret a difference quotient limit as the derivative at a point
  • use the limit definition to connect secant slopes with instantaneous rate

LIM-3.A—Interpret a limit as a definition of a derivative question 1

[Maximum number: 1]

lim⁡h→0sin⁡(π3+h)−sin⁡(π3)h\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{3}+h\right)-\sin \left(\frac{\pi}{3}\right)}{h} is

A

0

B

12\frac{1}{2}

C

1

D

32\frac{\sqrt{3}}{2}

E

nonexistent

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