(a) Using Lagrange's interpolation formula express the following func…

Question

(a) Using Lagrange's interpolation formula express the following function as a sum of partial fractions : $\frac{x^2 + 6x - 1}{(x^2 - 1)(x - 4)(x - 6)}$.

(b) Let $f(x) = x^2 e^x + 2x$. Then taking $x_0 = 1.5, x_1 = 1.55, x_2 = 1.62$, approximate $f(x)$ at $x = 1.52$ by Newton's divided difference formula. Compare the result with the actual value.

(c) Evaluate $\int_0^{\pi/2} \sqrt{\sin \theta} d\theta$ by Simpson's $\frac{1}{3}$ rule taking seven ordinates.