(a) Using Newton's divided difference formula, evaluate $f(9)$ from t…

Question

(a) Using Newton's divided difference formula, evaluate $f(9)$ from the following data :

$f(5) = 150, f(7) = 392, f(11) = 1452, f(13) = 2366, f(17) = 5202$.

(b) Using Newton-Raphson method, find a real root of $2x - \log_{10}x - 7 = 0$ correct to three decimal places.

(c) Using Trapezoidal rule, evaluate $\int_{0}^{5} \frac{1}{4x + 5} dx$ by taking 10 subintervals.

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