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Free response·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

t025710v(t)374−12The table gives velocity v(t) in meters per second.\begin{array}{c|ccccc}t&0&2&5&7&10\\ \hline v(t)&3&7&4&-1&2\end{array}\quad\text{The table gives velocity }v(t)\text{ in meters per second.}
Total: 5 points

(a) Use a left Riemann sum on the listed subintervals to approximate displacement on [0,10][0,10]. (2 points)

(b) Use the trapezoidal rule on the listed subintervals to approximate displacement on [0,10][0,10]. (2 points)

(c) Explain why these are displacement approximations, not total distance approximations. (1 point)

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