Chapter_02_(cont.) - Li Chen, Spring 2008 page 24 2-1. The...

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page 24 © Li Chen , Spring 2008 Chapter 2 2-1. The Tangents and Velocity Problems Definition The Average Rate of Change of a function y = f ( x ) between x = a to x = b is Ex 1. The total acreage of farms in the US has decreased since 1980. t (years) 1980 1985 1990 1995 2000 y (million acres) 1,039 1,012 987 963 945 (a) Find the average rate of change of farm land between 1980 and 2000. Give the units. (b) If P and Q are the points (1980, 1,039) and (2000, 945) on the curve of y , find the slope of the secant line between P and Q . (c) Can you estimate the slope of the tangent line at t = 1995? (d) Can you estimate the rate of change of farm land at year 1995? change in ( ) ( ) change in y y f b f a x x b a - = = -
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© Li Chen , Spring 2008 Chapter 2 The Average velocity Definition The average velocity of a moving object with a position function s ( t ) over a time interval [ a , b ] is defined: Ex 2. Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto. By Galileo’s law, the distance fallen by any freely falling body is expressed by the equation s ( t ) = 16 t 2 where s is in feet and t is in seconds. (a) Find the average velocity over the following time periods: [1, 3], [1, 1.5] and [1, 1+ h ]. (b) Find the velocity of the ball after one ( t = 1) second. a
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This note was uploaded on 04/19/2008 for the course MATH 1010 taught by Professor Don'tremeber during the Spring '08 term at Rensselaer Polytechnic Institute.

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Chapter_02_(cont.) - Li Chen, Spring 2008 page 24 2-1. The...

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