Decimal Place Accuracy

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Decimal Place Accuracy

As done in class, to find one decimal place accuracy take the right and leftsums using the same number of subintervals

  > rs:=evalf(rightsum(f(x),x=1..5,100));

$\begin{maplelatex} \begin{displaymath} rs:=45.81440000\end{displaymath}\end{maplelatex}$

  > ls:=evalf(leftsum(f(x),x==1..5,100));

$\begin{maplelatex} \begin{displaymath} ls:=44.8544000\end{displaymath}\end{maplelatex}$
The absolute value of their difference will give the accuracy. For one decimal place accuracy the absolute value of the difference should be less than 0.05.

  > rs-ls;

$\begin{maplelatex} \begin{displaymath} 0.96000000\end{displaymath}\end{maplelatex}$
Experimenting with the number of subintevals, the minimum number of subintevals needed is 192.

  > rs:=evalf(rightsum(f(x),x=1..5,1920));

$\begin{maplelatex} \begin{displaymath} rs:=45.35833622\end{displaymath}\end{maplelatex}$

  > ls:=evalf(leftsum(f(x),x==1..5,1920));

$\begin{maplelatex} \begin{displaymath} ls:=45.30833622\end{displaymath}\end{maplelatex}$

  > rs-ls;

$\begin{maplelatex} \begin{displaymath} 0.05000000\end{displaymath}\end{maplelatex}$

Christine M Palmer
3/24/1998