L06 - L6 The Tangent Line, Velocity Problems and Limits...

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Unformatted text preview: L6 The Tangent Line, Velocity Problems and Limits Tangent line to a circle. Tangent line to a curve. Slope Approximate slope 1 Let f ( x ) = x 2 + 1. Find the equation of the tangent line at (1 , 2). (1 , 2) and (1 . 1 , 2 . 21) approximate m = (1 , 2) and (1 . 01 , 2 . 0201) approximate m = 2 Let P be (1 , 2) and Q be ( x,x 2 + 1) approximate m tangent m Equation: 3 Velocity Suppose an object is s ( t ) feet from its start at t seconds. Find the average velocity on the time interval from t = 2 to t = 2 + h seconds where s ( t ) = 3 t 2 . Average Velocity = 4 Find the velocity at the instant 2 seconds. Instantaneous velocity = 5 Def lim x a f ( x ) = L if we can make the values of f ( x ) arbitrarily close to L by taking x sufficiently close to a but not equal to a . f ( x ) as x Consider f ( x ) = x 2- 1 x- 1 . Find lim x a f ( x ). x f ( x ) x f ( x ) 6 Sketch f ( x ). Consider g ( x ) = x 2- 1 x- 1 x 6 = 1 3 x = 1 Sketch g ( x ) and find lim x 1 g ( x )....
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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L06 - L6 The Tangent Line, Velocity Problems and Limits...

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