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AP®︎/College Calculus BC

Definite integral as the limit of a Riemann sum

AP.CALC: LIM‑5 (EU), LIM‑5.B (LO), LIM‑5.B.1 (EK), LIM‑5.B.2 (EK), LIM‑5.C (LO), LIM‑5.C.1 (EK), LIM‑5.C.2 (EK)

Which of the limits is equivalent to the following definite integral?

integral, start subscript, 1, end subscript, start superscript, e, end superscript, natural log, x, d, x

(Choice A)
limit, start subscript, n, \to, infinity, end subscript, sum, start subscript, i, equals, 1, end subscript, start superscript, n, end superscript, natural log, left parenthesis, 1, plus, i, dot, start fraction, e, minus, 1, divided by, n, end fraction, right parenthesis, dot, start fraction, e, minus, 1, divided by, n, end fraction
(Choice B)
limit, start subscript, n, \to, infinity, end subscript, sum, start subscript, i, equals, 1, end subscript, start superscript, n, end superscript, natural log, left parenthesis, i, dot, start fraction, e, minus, 1, divided by, n, end fraction, right parenthesis, dot, start fraction, e, minus, 1, divided by, n, end fraction
(Choice C)
limit, start subscript, n, \to, infinity, end subscript, sum, start subscript, i, equals, 1, end subscript, start superscript, n, end superscript, natural log, left parenthesis, 1, plus, start fraction, e, i, divided by, n, end fraction, right parenthesis, dot, start fraction, e, divided by, n, end fraction
(Choice D)
limit, start subscript, n, \to, infinity, end subscript, sum, start subscript, i, equals, 1, end subscript, start superscript, n, end superscript, natural log, left parenthesis, 1, plus, start fraction, i, divided by, n, end fraction, right parenthesis, dot, start fraction, e, divided by, n, end fraction

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