(a) Find Lagrange’s interpolating polynomial that fits the following data. Hence obtain the value of f(4).

To find Lagrange's interpolating polynomial for the given data and then calculate the value of \( f(4) \), we can use the Lagrange interpolation formula:

\[ P(x) = \sum_{i=0}^{n} f(x_i) \prod_{j=0, j\neq i}^{n} \frac{x - x_j}{x_i - x_j} \]

For the provided data:

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