Recall that, using left endpoints, the area A of the region that lies under the graph of the continuous function v is the limit of the sum of the areas of the n approximating rectangles as follows. A = lim L, n = lim vlt, Jat + v(e, )ar + .. ... Here we wish to find L, where At = 0.5. Therefore, we have the following. t = v(E,X0.5) + v(r,)(0.5) + v[t,)(0.5) + v(t,)(0.5) + v(t,(0.5) + v(r,)(0.5) We refer again to the given table. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.2 18.1 20.2 10.8 14.9 19.4 Substituting the appropriate values of v from the table gives us the following result. L =

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.