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Taylor Expansion: First and Second Order Approximations

Learn the concept of Taylor expansion and how to use first and second order approximations. Estimate position of points using derivatives.

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Taylor Expansion: First and Second Order Approximations

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  1. 30 m 2000 m 30 m 2000 m

  2. Wood per meter 2000 meters

  3. Taylor Expansion 180 160 140 ? 120 100 80 60 40 4.8 5 5.2 5.4 5.6 5.8 6 6.2

  4. Taylor Expansion 170 160 150 140 130 120 110 100 4.8 5 5.2 5.4 5.6 5.8 6 6.2 First order approximation – use first derivative Basically extend line from point 1 to estimate Position of point 2

  5. Taylor Expansion 170 160 150 140 130 120 110 100 4.8 5 5.2 5.4 5.6 5.8 6 6.2 Second order approximation – use first derivative and second derivative to estimate position of point 2

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