Numerical Metods Quiz

Which of the following is a transcendental equation?

• x³ - 2x + 1 = 0

• log x + x = 0

• x² + 4x + 4 = 0

• x⁴ - 1 = 0

Which method is used to find approximate solutions of algebraic and transcendental equations?

• Laplace transform

• Finite element method

• Iteration method

• Fourier series

The Iteration method converges if:

• |f'(x)| > 1

• |f(x)| < 1

• |g'(x)| < 1

• |g(x)| > 1

In fixed-point iteration, we express the equation f(x) = 0 as:

• x = f(x)

• f(x) = x

• x = g(x)

• f(x) = g(x)

In the iteration method, the next approximation is given by:

• x_n+1 = f(x_n)

• x_n+1 = x_n - f(x_n)/f'(x_n)

• x_n+1 = x_n + g(x_n)

Newton-Raphson formula is:

• x_n+1 = g(x_n)

• x_n+1 = x_n + f(x_n)/f'(x_n)

• x_n+1 = x_n - f(x_n)/f'(x_n)

• x_n+1 = x_n - f(x_n)

Which of the following is a backward difference operator?

• Δ

• ∇

• EE

• DD

The forward difference operator Δf(x) is defined as:

• f(x+h) - f(x)

• f(x) - f(x+h)

• f(x+h) + f(x)

• f(x) ⋅ f(x+h)

The operator Δ² f(x) is equal to:

• f(x+2h) - f(x)

• Δ(Δf(x))

• f(x+h)^2 - f(x)^2

• f(x+2h) - 2f(x+h) + f(x)

Newton's Forward Interpolation Formula is best suited when:

• Interpolation is near the end

• Interpolation is near the middle

• Interpolation is near the beginning

• Data points are unevenly spaced