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Math · Advanced Math
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29% L ubc.ca (1 point) In this problem you will calculate the area between f(x) 5x2 +7 and the x-axis over the interval [0, 3] using a limit of right-endpoint Riemann sums: Area limfx)Ar Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. a. We start by subdividing [0,3] into n equal width subintervals [xo-x! ], [xi , X2 ], . . . .[h-l ] each of width Δ. Express the width of each subinterval Ar in terms of the number of subintervals n b. Find the right endpoints X1-X2A3 of the first, second, and third subintervals [xo.xil.lxi.x2l.[x2.x3l and express your answers in terms ofn x1,x2,x33/n,6/n,9/n Enter a comma separated list.) c. Find a general expression for the right endpoint x of the kth subinterval xk-1 where 1 S k S n. Express your answer in terms of k and m d. Find f(xx) in terms of k and n fx)(45k2/n2)+7 e. FindfOxx)Ar in terms of k and n fax)Ar (21/n)+(3/n) (45k 2/n2) f. Find the value of the right-endpoint Riemann sum in terms of n g. Find the limit of the right-endpoint Riemann sum. 1-00
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