03_08slides(draft) - 3.8 examples Linear approximation...

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 examples Linear approximation, differentials, and the Newton-Raphson method Bradford Sanders March 11, 2016
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 1 Let f ( x ) = ln( x ). Approximate f (1 . 1) using the line tangent to the graph of y = f ( x ) where x = 1.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 2 Use a linear approximation to approximate 3 7 . 8.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 3 x n +1 = x n - f ( x n ) f ( x n ) Perform two iterations of the Newton-Raphson method to approximate a solution c to x 3 - 3 x
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