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AP®︎ Calculus AB (2017 edition)

Course: AP®︎ Calculus AB (2017 edition) > Unit 2

Lesson 4: Formal definition of the derivative as a limit

Derivative as a limit

AP.CALC: CHA‑2 (EU), CHA‑2.B (LO), CHA‑2.B.2 (EK), CHA‑2.B.3 (EK), CHA‑2.B.4 (EK)

Which of the following is equal to f, prime, left parenthesis, start fraction, pi, divided by, 2, end fraction, right parenthesis for f, left parenthesis, x, right parenthesis, equals, sine, left parenthesis, x, right parenthesis?

(Choice A)
limit, start subscript, x, \to, start fraction, pi, divided by, 2, end fraction, end subscript, start fraction, sine, left parenthesis, x, right parenthesis, minus, start fraction, pi, divided by, 2, end fraction, divided by, x, minus, 1, end fraction
(Choice B)
limit, start subscript, x, \to, start fraction, pi, divided by, 2, end fraction, end subscript, start fraction, sine, left parenthesis, x, plus, start fraction, pi, divided by, 2, end fraction, right parenthesis, minus, sine, left parenthesis, start fraction, pi, divided by, 2, end fraction, right parenthesis, divided by, x, minus, start fraction, pi, divided by, 2, end fraction, end fraction
(Choice C)
limit, start subscript, x, \to, start fraction, pi, divided by, 2, end fraction, end subscript, start fraction, sine, left parenthesis, x, right parenthesis, minus, sine, left parenthesis, start fraction, pi, divided by, 2, end fraction, right parenthesis, divided by, x, minus, start fraction, pi, divided by, 2, end fraction, end fraction
(Choice D)
limit, start subscript, x, \to, start fraction, pi, divided by, 2, end fraction, end subscript, start fraction, sine, left parenthesis, x, minus, start fraction, pi, divided by, 2, end fraction, right parenthesis, divided by, x, minus, start fraction, pi, divided by, 2, end fraction, end fraction

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AP®︎ Calculus AB (2017 edition)

Course: AP®︎ Calculus AB (2017 edition) > Unit 2

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