Single Variable Calculus, Chapter 5, 5.1, Section 5.1, Problem 12

Below are the table for the speedometer readings for a motorcycle at 12 second interval.

$
\begin{array}{|c|c|c|c|c|c|c|}
\hline\\
t(s) & 0 & 12 & 24 & 36 & 48 & 60 \\
\hline\\
v (ft/s) & 30 & 28 & 25 & 22 & 24 & 27\\
\hline
\end{array}
$

a.) Using the velocities at the beginning of the time intervals, estimate the distance travelled by the by the motorcycles during this time period.


$
\begin{equation}
\begin{aligned}

d =& 12 (30 + 28 + 25 + 22 + 24)
\\
\\
d =& 1548 ft

\end{aligned}
\end{equation}
$


b.) Give another estimate using the velocities at the end of the time periods.


$
\begin{equation}
\begin{aligned}

d =& 12 (28 + 35 + 22 + 24 + 27)
\\
\\
d =& 1512 ft

\end{aligned}
\end{equation}
$


c.) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

Since $v(t)$ is neither increasing nor decreasing function, the estimates are neither under estimates nor over estimates.

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