(a) Use the following definition to find an expression for the area under the curve y =x from 0 to 3 as a limit.The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas ofapproximating rectangles:lim Rnlim [f(x1)Ax + f(x2)Ax + . . . + f(xn)Ax]A =n → 003ilimiCloui = 1in()lim3i3Locan3in(oTaaslimn → 00A =n13ilimi = 0()33limni = 2n → 00(b) Use the following formula to evaluate the limit in part (a).13 + 23 + 33 ++ n3n(n + 1)]2Need Help?Read It

calculate the area under the curve.

a) Use the following definition to find an expression for the area under the curve y = x from 0 to 3 as a limit. The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas o approximating rectangles: A = lim Rn = lim [f(x1)Ax + f(x2)Ax + . . . + f(Xn)Ax] n- 00 3i O im n n 00 i = 1 O lim n- 00 i = 3 ΣΗ Ol im i = 1 O im n- 00 O im b) Use the following formula to evaluate the limit in part (a). 13 + 23 + 33 + . .. + n3 = [n(n + 1)]²

a) Use the following definition to find an expression for the area under the curve y = x from 0 to 3 as a limit. The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas o approximating rectangles: A = lim Rn = lim [f(x1)Ax + f(x2)Ax + . . . + f(Xn)Ax] n- 00 3i O im n n 00 i = 1 O lim n- 00 i = 3 ΣΗ Ol im i = 1 O im n- 00 O im b) Use the following formula to evaluate the limit in part (a). 13 + 23 + 33 + . .. + n3 = [n(n + 1)]²

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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