Consider the function $$ h(x)= \begin{cases}1 & \text { for } 0 \leq x 0$, construct a partition $P_{\epsilon}$ for which $U\left(f, P_{\epsilon}\right)<1+\epsilon$. \end{enumerate}

Exercise 7.3.1

Consider the function

h (x) = {\begin{matrix} 1 & for 0 \leq x < 1 \\ 2 & for x = 1 \end{matrix}

over the interval $[0, 1]$ .

(a): Show that $L (f, P) = 1$ for every partition $P$ of $[0, 1]$ .
(b): Construct a partition $P$ for which $U (f, P) < 1 + 1 ∕ 10$ .
(c): Given $𝜖 > 0$ , construct a partition $P_{𝜖}$ for which $U (f, P_{𝜖}) < 1 + 𝜖$ .

TODO

ulissemini

2022-01-27 00:00