Question: For Problems 2 and 3, find the natural cubic splines that pass through the given data points. Use the splines to answer the requirements. 2.

For Problems 2 and 3, find the natural cubic splines that pass through the given data points. Use the splines to answer the requirements. 2. x 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 y 20.08 22.20 24.53 27.12 29.96 33.11 36.60 40.45 44.70 49.40 a. Estimate the derivative evaluated at x = 3.45. Compare your estimate with the derivative of ex evaluated at x = 3.45. b. Estimate the area under the curve from 3.3 to 3.6. Compare with 3.6 / ex dx 3.3 3. x 0 JT/6 31/3 It/2 231/3 SiT/ It y 0.00 0.50 0.87 1.00 0.87 0.50 0.00

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