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Numerical-methods Questions Set 1:

Quiz Mode

What is the order of convergence of the Bisection Method?

1/2

3/2

Solution:

Which of these methods is the slowest to converge?

Newton-Raphson

Regula-Falsi

Bisection

Secant

Solution:

Using the one-step Newton-Raphson method to solve the equation x⁴ - 3x + 10 = 0, starting from x = 1, the next value of x is:

-7

-3

Solution:

The real root of the equation cos(x) - 3x + 1 = 0, correct to seven decimal places by Newton-Raphson's method, is:

0.6071016

0.6071018

0.6071116

0.6071106

Solution:

If f(x) is continuous in [a,b], then the necessary condition for a root to lie in the interval [a,b] is

None of these

f(a)·f(b) < 0

f(a)·f(b) > 0

f(a)·f(b) = 0

Solution:

The approximate root of the equation x = 1/a using the Newton-Raphson method is

x_k+1 = x_k - a(x_k)²/2

x_k+1 = (x_k + a/x_k)/2

x_k+1 = (x_k + a(x_k)²/2)

x_k+1 = 2x_k - a(x_k)²

Solution:

The First Approximation of the root of f(x) using the Newton-Raphson method is given by:

x1 = x0 + f'(x).f(x)

x1 = x0 - (f(x)/f'(x))

x1 = x0.f'(x)/f(X)

x1 = x0 + (f'(x)/f(x))

Solution:

Let x² - 117 = 0. The iterative steps for the solution using Newton-Raphson's Method is given by:

xn+1 = (xn + 117/xn)

xn+1 = (xn + 117/xn)/2

xn+1 = (1 + 117/xn)/2

xn+1 = (xn - 117/xn)/2

Solution:

Which of the following statements about the Gauss-Seidel method is false?

This method guarantees convergence

Iteration Method is self-correcting

The iteration is stopped when the values of x, y, z start repeating with the required degree of accuracy

None of the above

Solution:

The table below gives values of a function f(x) obtained for values of x at intervals of 0.25. The value of the integral of the function between the limits 0 and 1 using Simpson's rule is (up to 4 decimal places):

X 0 0.25 0.5 0.75 1.0

F(x) 1 0.942 0.8 0.64 0.50

0.7854

2.3562

3.1416

7.5000

Numerical-methods Questions Set 1:

What is the order of convergence of the Bisection Method?

Solution:

Which of these methods is the slowest to converge?

Solution:

Using the one-step Newton-Raphson method to solve the equation x⁴ - 3x + 10 = 0, starting from x = 1, the next value of x is:

Solution:

The real root of the equation cos(x) - 3x + 1 = 0, correct to seven decimal places by Newton-Raphson's method, is:

Solution:

If f(x) is continuous in [a,b], then the necessary condition for a root to lie in the interval [a,b] is

Solution:

The approximate root of the equation x = 1/a using the Newton-Raphson method is

Solution:

The First Approximation of the root of f(x) using the Newton-Raphson method is given by:

Solution:

Let x² - 117 = 0. The iterative steps for the solution using Newton-Raphson's Method is given by:

Solution:

Which of the following statements about the Gauss-Seidel method is false?

Solution:

The table below gives values of a function f(x) obtained for values of x at intervals of 0.25. The value of the integral of the function between the limits 0 and 1 using Simpson's rule is (up to 4 decimal places):

X 0 0.25 0.5 0.75 1.0

F(x) 1 0.942 0.8 0.64 0.50

Solution:

Related Question Sets:

Related Topics:

Numerical-methods Questions Set 1:

What is the order of convergence of the Bisection Method?

Solution:

Which of these methods is the slowest to converge?

Solution:

Using the one-step Newton-Raphson method to solve the equation x4 - 3x + 10 = 0, starting from x = 1, the next value of x is:

Solution:

The real root of the equation cos(x) - 3x + 1 = 0, correct to seven decimal places by Newton-Raphson's method, is:

Solution:

If f(x) is continuous in [a,b], then the necessary condition for a root to lie in the interval [a,b] is

Solution:

The approximate root of the equation x = 1/a using the Newton-Raphson method is

Solution:

The First Approximation of the root of f(x) using the Newton-Raphson method is given by:

Solution:

Let x2 - 117 = 0. The iterative steps for the solution using Newton-Raphson's Method is given by:

Solution:

Which of the following statements about the Gauss-Seidel method is false?

Solution:

The table below gives values of a function f(x) obtained for values of x at intervals of 0.25. The value of the integral of the function between the limits 0 and 1 using Simpson's rule is (up to 4 decimal places): X 0 0.25 0.5 0.75 1.0 F(x) 1 0.942 0.8 0.64 0.50

Solution:

Related Question Sets:

Related Topics:

Using the one-step Newton-Raphson method to solve the equation x⁴ - 3x + 10 = 0, starting from x = 1, the next value of x is:

Let x² - 117 = 0. The iterative steps for the solution using Newton-Raphson's Method is given by:

The table below gives values of a function f(x) obtained for values of x at intervals of 0.25. The value of the integral of the function between the limits 0 and 1 using Simpson's rule is (up to 4 decimal places):

X 0 0.25 0.5 0.75 1.0

F(x) 1 0.942 0.8 0.64 0.50