Answer
(a) $\frac{1}{2}$
(b) $1, 2, \frac{3}{2}, \frac{5}{2}$
(c) $\frac{5}{4}, \frac{7}{4}, \frac{9}{4}, \frac{11}{4}$
(d) $2,3, \frac{5}{2}, \frac{3}{2}$
Work Step by Step
(a) The interval has length $2,$ so: $\frac{1}{2}=\frac{2}{4}$
(b) The intervals are then $\left[2, \frac{5}{2}\right], \left[1, \frac{3}{2}\right],\left[\frac{3}{2}, 2\right]$ and $\left[\frac{5}{2}, 3\right]$
So the left end points are: $1, \frac{3}{2}, 2, \frac{5}{2}$
(c) The intervals are then $\left[1, \frac{3}{2}\right],\left[\frac{3}{2}, 2\right],\left[2, \frac{5}{2}\right]$ and $\left[\frac{5}{2}, 3\right]$
Thus the midpoints are: $\frac{5}{4}, \frac{7}{4}, \frac{9}{4}, \frac{11}{4}$
(d) The intervals are then $\left[\frac{3}{2}, 2\right],\left[2, \frac{5}{2}\right], \left[1, \frac{3}{2}\right]$ and $\left[\frac{5}{2}, 3\right]$
So the left end points are: $\frac{3}{2}, 2, \frac{5}{2}, 3$
