1. An object's velocity is measured as a function of time.
2.
Let
Sketch the graph of F(x) over the interval (a , b).
3. Given
Find formulas for v(t) and y(t). Include your constants of integration. Interpret these constants of integration.
Using these formulas, find when a water balloon which is launched upward with an initial velocity of 50ft/sec from the top of a stadium, which is 40ft above the ground, hits the ground. What is its velocity when it hits the ground?
4. The rate at which the population of a town is increasing is 3% per year. i.e.,
where the population, P, is measured in people and the time, t, is measured in years.
Solve this differential equation to get the population as a function of time. If we start measuring the time now (i.e., t = 0 at the present) and the population of the town is 30,000 people now, what will the population be in 5 years?
5. Find the following indefinite integrals. 5a, 5b, 5c, 5d.
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6. Find the following definite integrals.
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