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tutorial_wk10 - Tutorial week 10 1. A dierentiable function...

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Unformatted text preview: Tutorial week 10 1. A dierentiable function takes the values f (-. 1) =-1 . 629 , f (0) =-1 . 312 and f (0 . 1) =-1 . 043 . Using the central and backward dierence formulae f ( x 2 )-f ( x ) x 2-x and f ( x 1 )-f ( x ) x 1-x estimate f (0). Which do you think will be the more accurate estimate, and why? ANSWER: Using the central dierence formula with x 2 = 0 . 1 and x =-. 1 f (0) -1 . 043-(-1 . 629) . 1-(-. 1) = 2 . 93 . Using the backwards dierence formula with x 1 = 0 and x =-. 1 f (0) -1 . 312-(-1 . 629)-(-. 1) = 3 . 17 . As the central dierence is second order and the forwards dierence formula is rst order, the central dierence formula will be best. 2. Use appropriate approximations to estimate f ( x ) for each value of x in the table below. Which do you think is the most accurate approximation, and why? x . 49 . 50 . 51 f ( x ) 1 . 11294 1 . 11730 1 . 12171 ANSWER: For f (0 . 5) the second-order central dierence formula gives: f (0 . 5) 1 . 12171...
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tutorial_wk10 - Tutorial week 10 1. A dierentiable function...

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