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Unformatted text preview: Lecture 11 (Section 2.7): Tangents, Velocities and Rates of Change 6 ? Def. The tangent line to y = f ( x ) at the point P ( a;f ( a )) is the line through P with slope m = provided that the limit exists. NOTE: Slope of the curve y = f ( x ) at the point ( a;f ( a )): ex. Find the equation of the tangent line to y = x 3 at the point (2 ; 8). 6 ? Alternate De nition of the Slope of a Tangent Line Let h = x a . Then and m = ex. Find the equation of the tangent line to y = 1 x 2 at x = 4. 6 ? ex. Find the slope of the tangent line to y = p 10 3 x at x = a . 1) at x = 2 m = 2) at x = 1 3 m = 3) at x = 5 m = Velocity Suppose an object moves along a straight line according to an equation of motion s = f ( t ) where s is the displacement (directed distance) from the starting point at time t . We call f ( t ) the position function of the object. Average Velocity on interval t = a to t = a + h NOTE: This is the same as the slope of the secant line through ( a;f ( a )) and ( a + h;f ( a + h ))....
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This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL

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