1) For the function f(x) = x2 + 3, find a formula for the upper sum obtained by dividing the interval [0, 3] into n equal subintervals. Then take the limit as n→∞ to calculate the area under the curve over [0, 3]
2) For the function f(x) = 36 – x2 , find a formula for the Riemann sum obtained by dividing the interval [0,6] into n equal sub intervals and using the right-hand endpoint for each Ck. Then take a limit of these sums as n–>infinity to calculate area under the curve
3)Use finite approximations to estimate the area under the graph of the function f(x) = 25 – x^2
between x = -5 and x = 5 using
-
(a) a lower sum with two rectangles of equal width
-
(b) a lower sum with four rectangles of equal width,
-
(c) an upper sum with two rectangles of equal width,
-
(d) an upper sum with four rectangles of equal width.
0 comments