Exercise 4.2.4

Question

Consider the reasonable but erroneous claim that
  $$
  \lim _{x \rightarrow 10} 1 /[[x]]=1 / 10
  $$
  \begin{enumerate}[label=(\alph*)] 
  \item Find the largest $\delta$ that represents a proper response to the challenge of $\epsilon=1 / 2$
  \item Find the largest $\delta$ that represents a proper response to $\epsilon=1 / 50$.
  \item Find the largest $\epsilon$ challenge for which there is no suitable $\delta$ response possible.
   \end{enumerate}

Ulisse Mini · Accepted Answer

\begin{enumerate}[label=(\alph*)] 
  \item $\delta = 13$
  \item $\delta = 1$
  \item No matter how small $\delta$ is, $[[10-\delta/2]] = 9$ can be obtained, meaning
    $$
    |1/9 - 1/10| = 1/90
    $$
    Is the largest $\epsilon$ with no suitable $\delta$ response.
   \end{enumerate}

Exercise 4.2.4

Answers

Comments

Exercise 4.2.4

Answers

Comments

Add answer