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Let f (x) = 3xex − e2x.
a. Approximate f (1.03) by the Hermite interpolating polynomial of degree at most three using x0 = 1 and x1 = 1.05. Compare the actual error to the error bound.
b. Repeat (a) with the Hermite interpolating polynomial of degree at most five, using x0 = 1, x1 = 1.05, and x2 = 1.07. |
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