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Unformatted text preview: at x = 1 (accurate upto at least 8 digits). Assuming that this results is true, nd the absolute errors for all the methods above. 3. (3 pts.) Consider the following numerical differentiation formula: f ( x ) f ( x + h ) + f ( x-2 h ) h Find the appropriate values for , and for this formula to work (using Taylor series expansion). What is the order of your approximation? 4. (3 pts) Consider the following numerical differentiation formula: f ( x ) -f ( x + 2 h ) + 8 f ( x + h )-8 f ( x-h ) + f ( x-2 h ) 12 h Prove that this is a valid formula (using Taylors expansion) and nd its order. 1 Note that x is in radians, that is, sin ( 2 ) = 1. 1...
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This note was uploaded on 09/19/2010 for the course ENGR 6310 taught by Professor Caner during the Fall '10 term at University of Georgia Athens.
- Fall '10