Construct a natural cubic spline to approximate f (x) = ex by using the values given by

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Construct a natural cubic spline to approximate f (x) = eˆ’x by using the values given by f (x) at x = 0, 0.25, 0.75, and 1.0. Integrate the spline over [0, 1], and compare the result to
Se dx = 1- 1/e.

Use the derivatives of the spline to approximate f'(0.5) and f'' (0.5). Compare the approximations to the actual values.

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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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