26Chapter 2 Instantaneous Rate Of Change: The DerivativeExercises1.An object is traveling in a straight line so that its position (that is, distance from some fixedpoint) is given by this table:time (seconds)0123distance (meters)0102560Find the average speed of the object during the following time intervals: [0,1], [0,2], [0,3],[1,2], [1,3], [2,3].If you had to guess the speed att= 2 just on the basis of these, whatwould you guess?⇒2.Lety=f(t) =t2, wheretis the time in seconds andyis the distance in meters that anobject falls on a certain airless planet.Draw a graph of this function betweent= 0 andt= 3. Make a table of the average speed of the falling object between (a) 2 sec and 3 sec,(b) 2 sec and 2.1 sec, (c) 2 sec and 2.01 sec, (d) 2 sec and 2.001 sec. Then use algebra to finda simple formula for the average speed between time 2 and time 2 + Δt. (If you substituteΔt= 1,0.1,0.01,0.001 in this formula you should again get the answers to parts (a)–(d).)
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