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AP Calculus BC 2.1: Derivative as a Limit

Practise AP Calculus BC 2.1 questions by recognising difference-quotient limits as derivatives and evaluating an instantaneous rate of change at a point.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • Recognise a difference-quotient limit as f′(a), then evaluate the derivative at the stated point.

CHA-2.B—Represent the derivative of a function as the limit of a difference quotient question 1

[Maximum number: 1]

lim⁡h→025+h−5h\lim _{h \rightarrow 0} \frac{\sqrt{25+h}-5}{h}

A

(A)=0(\mathrm{A})=0

B

(B) =110=\frac{1}{10}

C

(C) =1

D

(D) does not exist

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