Write out the Riemann Sum for R(f,P, 0, 2) for arbitrary n, f(x) = x2+/-3x+2, where each ∆xk = 2/n and ck = xk, simplify and use the formulas ∑n,k=1
k=(n(n+1))/2 and ∑n,k=1 k2=n((n + 1)(2n + 1))/6 to find the limit as n --> 1.
Solution. We know that ∆xk = 2/n and ck = xk=2k/n, k=1,2,...,n(x0=0,x1=2/n,x2=4/n,...,xn=2). f(x) = ...
A Riemann sum is found and a limit is obtained. The limits of the functions are determined.