• Attempt any five questions.
• All questions carry equal marks.
Evaluate √12 to four decimal places by Newton Raphson Method.
What is the rate of convergence of bisection method?
Prove the relations between finite difference operators Δ, δ, and ∇.
Construct a backward difference table for y = log x and find values of ∇³log 40 and ∇⁴log 50.
Using Lagrange's Method find f(x) as a polynomial in x from the given data.
Using Newton's divided difference formula, calculate the value of f(6) from the given data.
Find f'(1.1) and f''(1.1) from the given table.
Find missing values in the given table.
Find ∫₀⁶ e^x/(1+x) dx approximately using Simpson's 3/8th rule.
Solve dy/dx = 1 - y with y(0)=0 using Euler's modified method at x=0.1,0.2,0.3.
Using Lagrange's interpolation formula to fit a polynomial to the given data.
Using Regula-Falsi method, find the real root of x log₁₀ x = 1.2 correct to four decimal places.
Solve dy/dx = x + y² by Runge-Kutta method of fourth order for y at x=0.2, given y=1 at x=0, h=0.1.
Evaluate L⁻¹[(s+7)/(s²+4s+8)].
Find the inverse Laplace transform of (s+4)/[s(s-1)(s²+4)].
Prove that L{f(t)/t} = ∫_s^∞ F(s) ds and hence evaluate (e^(at) - cos bt)/t.
