Math / Calculus

QuestionThe velocity $v(t)$ in the table below is increasing for $0 \leq t \leq 12$ . \begin{tabular}{|c|c|c|c|c|c|} \hline $t$ & 0 & 3 & 6 & 9 & 12 \\ \hline $v(t)$ & 32 & 36 & 39 & 40 & 44 \\ \hline \end{tabular} A. Find an upper estimate for the total distance traveled using $n=4$ subdivisions: distance traveled = $\square$ $n=2$ subdivisions: distance traveled = $\square$ B. Which of the two answers in part (A) is more accurate? $n=$ $\square$ is more accurate (Be sure that you can explain why!) C. Find a lower estimate for the total distance traveled using $n=4$ . distance traveled $=$ $\square$

Studdy Solution
For the lower estimate using $n=4$ subdivisions, use the Left Endpoint method:
$\text{Lower Estimate} = v(0) \cdot 3 + v(3) \cdot 3 + v(6) \cdot 3 + v(9) \cdot 3$ $= 32 \cdot 3 + 36 \cdot 3 + 39 \cdot 3 + 40 \cdot 3$ $= 96 + 108 + 117 + 120 = 441$
The solutions are: A. Upper estimate for $n=4$ : $477$ Upper estimate for $n=2$ : $498$ B. $n=4$ is more accurate. C. Lower estimate for $n=4$ : $441$

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