An object is dropped from a high cliff, and the distance (in feet) it has fallen after t seconds is given by the function  d(t) = 16t2.  Complete the table to find the average speed during the given time intervals. t = a t = b Average speed =  d(b) − d(a)/b-a   6 6.5   6 6.1   6 6.01   6 6.001   6 6.0001   Use the table to determine what value the average speed approaches as the time intervals get smaller and smaller. Is it reasonable to say that this value is the speed of the object at the instant  t = 6?  Explain. From the table it appears that the average speed approaches  ft/s

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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.