Thanks for helping. I keep confusing myself. I think the exponent keeps throwing me off.

For ????(????)=2+????², partition the interval [0, 4] into n equally wide sub intervals of length ?x = 4.

(a)Write the lower sum for this function and partition and calculate the limit of the lower sum as n ??.

(b)Write the upper sum for this function and partition and find the limit of the upper sum as n ??.

So far I have

1) For f (x)=2+x2, partition the interval [0, 4] into n equally wide subintervals of length Ax = 4. Ax = (b - a) (4-0) n n n 4 Xi = -i and f(x;) = 2 + x; =2+ (-i) (power rule, 2*product rule) = 2 + 1612 n2 (a) Write the lower sum for this function and partition and calculate the limit of the lower sum as f(x) is increasing in the given interval, the minimum value of f(x) in each subinterval will be at the left edge of that subinterval, so mi = Xi-1 n L = > f ( m;) Ax = > f (x;-1)Ax= 2 + 16 1- 1 12-1 ) ) i-1 16 n 2 1 1-1 = 1- 1 (2) + 69) EG) i-1 4 n(n + 1)] 2 (b) Write the upper sum for this function and partition and find the limit of the upper sum as n -00