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Unformatted text preview: th Taylor polynomial of f ( x ) based at a = 0. Simplify your answer as much as possible. (c) Find f (6) (0). 3 3. (15pts) Let f ( x ) = 2cos 2 x1. (a) Find the quadratic approximation T 2 ( x ) of f ( x ) based at a = 0 (b) Use the quadratic approximation to estimate f ( π 8 ). (c) Using Taylor’s inequality, ﬁnd the error bound for the estimate you computed in (b). 4 4. (15pts) Let A = (3 , , 0), B = (0 , 4 , 0), and C = (0 , , 1). (a) Find the area of the triangle ABC Hint. The following indentity may be useful: 3 2 + 4 2 + 12 2 = 13 2 . (b) Let CH be the height of the triangle from the vertex C to the base AB . Find the coordinates of the point H . 5...
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 Spring '07
 Smith
 Math, Taylor Series, quadratic approximation

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