Definition: 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 of approximating rectangles A = lim Rn = lim [f(x1)Ax + f(x2)Ax + · … + f(xn)Aæ]. n00 n00 (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x° from a = 0 to z = 1. A. lim n00 3 1 B. lim i=1 1 C. lim S n 5 D. lim nH00 i=1 (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula for the sum of cubes helpful: n(n+1 13 + 23 + 33 +……+n³ =

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A: Topic = Limit

Q: The area A of the region S that lies under the graph of the continuous function is the limit of the…

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Q: The area A of the region S that lies under the graph of the continuous function is the limit of the…

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Q: - check if the function is continuous 2- find if the limit exist

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Q: b) Write down the domain and range of the function y = f(x) graphed below. Which of the following…

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Q: (c) x³ - y³ lim (x,y)→(1,1) X-y

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Q: (a) Express the area under the curve y =x4 +5x2 +xfrom 2 to 7 as a limit.(b) Use a computer algebra…

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

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