# MTH 141 Final: Math 141 Final Exam V2

## Document Summary

Math 1830- final exam - december 14, 2006. 3 9 v2 dv: r 3. 2 t(3 t)1/3 dt: r 3. 0: (15 points) evaluate the riemann sum for with six equal intervals and taking your sample points to be the left endpoint of each interval. Explain, with the aid of a diagram, what the riemann sum represents. f (x) = x2 x. 0 x 3: (15 points, find the area under the graph of y = x2 + 2 and above the interval [1, 2] on the x axis, let f (x) = x2. Find the average value of f on the interval [2, 5]. Then nd a value c [2, 5] such that fave = f (c): (20 points) you are given g(x). Find the derivative g (x): g(x) = x sin(x, g(x) = sin x x2+1, g(x) = r x. 1 t2 + cos t dt: g(x) = r 1/x. 243 : limn pn i=1 sin( i.