Single Variable Calculus

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

Expert Answers

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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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