4. Given data of f(x) = ln(e" +2) in the following table -1 -0.5 0.5 f(x) | 0.86199480 0.95802009 | f'(x) | 0.15536240 | 0.23269654 | 0.33333333 0.45186776 1.0986123 1.2943768 (i) Construct the Lagrange interpolating polynomial of degree three and use it to approximate f(0.25); (ii) Construct the Hermite interpolating polynomial of degree five (through using xo = -0.5, x1 = 0 and x2 = 0.5) and use it to approximate f(0.25). %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.