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bananaslugs
bananaslugs
04.11.2019 • 
Mathematics

2. we derived a centered difference method for f′(x0) in class. in it, we used x0, x0+h, and x0−h to approximate f′(x0) with o(h2) accuracy. suppose we have the following data, and we want to estimate f′(x) at all points: 1.0 1.21.4 (z) 10.84 1.118 1.38 1.60 1.75 | 1.8 3 f (r)a) (1 point) you can’t use the centered difference method to estimate f′(1.0) and f′(1.8). why not? (b) (4 points) derive the following one-sided, three-point difference formula.the derivation will involve the 2nd degree taylor polynomial evaluated at x0+h and x0+ 2h. clearly show the o(h2) in your derivation.(c) (1 point) we could just use a forward/backward difference to approximate f′(1.0) and f′(1.8). why is this three-point difference formula better than the forward difference formula? (d) (3 points) we will use centered differences wherever possible, and the three-point one-sided difference where necessary (using a negative h in the one-sided difference can be useful). use a calculator to fill in the blanks using second order difference methods.

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