• Attempt any five questions.
• All questions carry equal marks.
If f(x)=x³-x²+4x-4=0, find next approximation from x=2 correct up to 2 decimal places.
What is the rate of convergence of Newton Raphson method?
Find Δe^(ax), Δ²e^x, Δlog x.
Prove that f(4) = f(3) + Δf(2) + Δ²f(1) + Δ³f(1) taking 1 as the interval of differencing.
Using Simpson's 3/8 rule to solve the integral ∫₄⁵·² log_e x dx.
Find f(0.18) from the given table using Newton's Forward interpolation formula.
Apply Gauss Elimination method to solve: 2x-y+3z=9, x+y+z=6, x-y+z=2.
Find missing values in the given table.
Use Runge-Kutta method to approximate y at x=0.1,0.2, given y=1 at x=0 and dy/dx=x+y.
Use Milne's method to solve dy/dx=x+y with y(0)=1 from x=0.20 to x=0.30.
Find the value of f(5) from the given table using interpolation.
Find the real root of x log₁₀ x - 1.2 = 0 correct to five decimal places by Regula Falsi Method.
Find the inverse Laplace transform of (2s+1)/[s(s-1)].
State convolution theorem and evaluate L⁻¹[s/{(s²+1)(s²+4)}].
A binomial variable X satisfies 9P(X=4)=P(X=2) when n=6. Find p and P(X=1).
Find the percentage of measurements between 54.8" and 68.8" for N(65.5, 6.2²).
