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x 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 y 20.08 22.2 24.53 27.12 29.96 33.11 36.6 40.45 44.7 49.4 Using cubic splines
x 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 y 20.08 22.2 24.53 27.12 29.96 33.11 36.6 40.45 44.7 49.4
x | 3 | 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 3.6 | 3.7 | 3.8 | 3.9 |
y | 20.08 | 22.2 | 24.53 | 27.12 | 29.96 | 33.11 | 36.6 | 40.45 | 44.7 | 49.4 |
Using cubic splines based on the Lagrange interpolation formula:
i) estimate derivative at x=3.45. Compare with the estimate with derivative of ex at x=3.45.
ii) Estimate area under the curve from 3.3 to 3.6. Compare with3.33.6exdx
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