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Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) using the following values. Find an error bound for the approximation.

cos(.6980) = 0.7661

cos(.7330) = 0.7432

cos(.7680) = 0.7193

cos(.8030) = 0.6946

The actual value of cos(.7500) = 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.

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Solution:

The approximation of cos(.7500) 0.7313. The actual error is 0.0004, and an error bound is 2.7 × 10

^{-8}. The discrepancy is due to the fact that the data are given only to four decimal places.

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Can anyone help me figure out the intermediary steps from the problem to solution?