67. An early limit Working in the early 1600s, the mathematicians Wallis, Pascal, and Fermat wanted to calculate the area of the region under the curve y = x² between x = 0 and x = 1, where p is a positive integer. Using arguments that predated the Fundamental Theorem of Calculus, they were able to prove that = 2 (+)² = p + ₁² Use what you know about Riemann sums and integrals to verify this limit.

67. An early limit Working in the early 1600s, the mathematicians Wallis, Pascal, and Fermat wanted to calculate the area of the region under the curve y = x² between x = 0 and x = 1, where p is a positive integer. Using arguments that predated the Fundamental Theorem of Calculus, they were able to prove that = 2 (+)² = p + ₁² Use what you know about Riemann sums and integrals to verify this limit.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.6: Permutations

Problem 47E

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