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Page 5 - So1ting Number I ES b(3 points For the...

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Unformatted text preview: So1ting Number: \ I ES b) (3 points) For the Newton—Raphson method of rootfinding, it is often necessary to use finite differencing to calculate a first derivative. The x-y data points below represent points sampled from an unknown function: 0.0000 —1.0000 0.1000 -0.9940 0.2000 09,721 I k I K: ~ 0.7000 —0.4218‘ 0.8000 —0. 1847 0.9000 0.1074 1.0000 0.4597 ‘\ 1w ‘ 4‘ We would like to find the dy/dx, the slope of this unknown function, at x = 0.5. The true value of the slope at x = 0.5 is 1.229. Use forward differencing with a step size of 0.1 to estimate the slope at x = 0.5. Report your answer and the associated true percent error to four significant 1 digits. "“‘““““"“"“ j “=4 1 h . m1 , (/ X‘ ’5 “(we dy/dxl.=o.5= laws-1‘0 ‘ “HM“ / ' [ALT \ffiwt, “@wao ”'5’: 59" "1(3) ‘ .124- 1.14330 Moo: ' lilzq ,u Nam“ . ”W" " ' . V I. c) (3 pomts For the same data, se central ifferefi’crng With a step Size 0 to estlrnate the ‘1 slope at x = 0.5. Report your answer and the associated true percent error to four significant diglts. , (J06): fulfill 'EUC'D ’2. h . X” ° g _, / )(C*L: ac XC’L::L‘ M Wu: 9 _ ’ . FT «harp—.1004?) 4299’s) 5 Fall 2009 7 f .11 [d d)’/dx|x=o.s= LU‘W ...
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