Textbook Problem

For the interval (0, 2]. determine whether the following statements are true or false.

(a) For 4 subintervals, each subinterval has width $\frac{1}{2}$.

(b) For 200 subintervals, each subinterval has width $\frac{1}{100}$.

(c) For n subintervals, each subinterval has width $\frac{2}{n}$.

(d) For n subintervals, $x_0=0,x_1=\frac{2}{n},x_2=2\left(\frac{2}{n}\right),...,x_i=i\left(\frac{2}{n}\right),...,x_n=2$.