In this problem you will calculate the area between f x 3r

Last updated: 4/26/2023

In this problem you will calculate the area between f x 3r and the z axis over the interval 0 2 using a limit of right endpoint Riemann sums 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 2 into n equal width subintervals zo 21 2 22 2 1 Zn each of width Az Express the width of each subinterval Az in terms of the number of subintervals Az b Find the right endpoints 21 22 23 of the first second and third subintervals zo 1 1 2 2 z3 and express your answers in terms of n 246 n n n 1 72 73 21 HT c Find a general expression for the right endpoint z of the kth subinterval 1 2 where 1 k n Express your answer in terms of k and n 24 11 d Find f z in terms of k and n f zk k3 13 e Find f z Az in terms of k and n f z Az lim 11 00 48 Enter a comma separated list k3 Area lim 8 4 f Find the value of the right endpoint Riemann sum in terms of n f 2x Az 12 g Find the limit of the right endpoint Riemann sum f xx Az 12