Consider the function f(x) = * +7. x² In this problem you will calculate +7) dx by using the definition 3 f(x) dx = lim f(x;)Ax n-00 The summation inside the brackets is R, which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub- interval. Calculate R, for f(x) = +7 on the interval [0, 4] and write your answer as a function of n without any summation signs. Hint: R, = lim R, = n-00 X; = 4i and Ax = .

Compute the average rate of change in the function f(x)= x³ + 7x²-12 on the interval [4, 6]. O 146 units of ffor every one-unit increase in x O-146 units of ffor every one-unit increase in x 310 units of ffor every one-unit increase in x O-310 units of ffor every one-unit increase in x

Consider the function f(x) = −²+ +4. 4 x² In this problem you will calculate ["(-33 0 = The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the right- hand endpoints of each sub-interval. Calculate Rn for f(x) = - + 4 on the interval [0, 4] and write your answer as a function of n without 3 signs. R₂ lim Rn n→∞ = +4) dx by using the definition ← ·b ["* ƒ(2) dx = lim [ƒ(2.)Az] n→∞ any summation