P06 - Project 6 MAC 2311 1 restricted to the x 1 In this...

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Project 6 MAC 2311 1. In this problem, we will use the function f ( x ) = 1 x restricted to the domain (0 , ). Give a quick sketch of the function f ( x ) on the axes below, and label the points on the graph that correspond to x = 1 2 , x = 1, x = 3 2 , and x = 2. Call these points A , B , C , and D respectively. Draw the lines between points A and D , between points B and D , and between points C and D . Then calculate the slope of each of the three lines. Are the above slopes enough information to deduce the exact slope of the tangent line at point D ? Make a guess below. Let’s calculate the slope of the tangent line at point D using limits: If you take point D and another generic point ( x,f ( x )) on the curve, then what is the slope m ( x ) of the line between them in terms of x ? Simplify your formula. What value does the slope approach as you choose the generic point closer and closer to D (by making x closer and closer to 2)? Write the equation of the line tangent to the graph of
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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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P06 - Project 6 MAC 2311 1 restricted to the x 1 In this...

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