Question

The interval [0,5] is partitioned into n equal subintervals, and a number xi is defined to be the left-hand endpoint of the i^th subinterval for each i. Then: limit as n approaches ∞ Σ with n-1 on top and i=0 on bottom for ((8xi)/n) is equal to what?

Answer 1

xi = 5/n, right? so you have

n-1
∑ (8xi)/n = (8*(5/n)i)/n = 40/n^2 i
i=0
This is a left Riemann sum
as an integral, that would be
∫[0..5] 8/5 x dx
because
(8xi)/n = (8/5 xi) * 5/n