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Numerical-methods Questions Set 3:

Quiz Mode

If μ is the mean of the distribution, then Σf_i(x_i - μ) is

Median

Standard Deviation

None of these

Solution:

What is the condition of failure for the Newton-Raphson method?

f'(x) = 0

f'(x) < 0

f'(x) > 0

This method does not fail

Solution:

Which of these is not a numerical integration method?

Trapezoidal Rule

Simpson's One-Third Rule

Simpson's 3/8th Rule

Runge-Kutta Method

Solution:

If e⁰ = 1, e¹ = 2.72, e² = 7.39, e³ = 20.09, and e⁴ = 54.60, then the value of the integral ∫₀⁴ e^x dx using Simpson's 1/3 rule is:

52.78

5.278

53.87

5.387

Solution:

The approximate root after n+1 iterations of the function x = e^-x using the Newton-Raphson method is:

x_n+1 = e^-x_n

x_n+1 = x_n - e^-x_n

x_n+1 = (1+x_n) e^-x_n/(1 + e^-x_n)

x_n+1 = 1 + e^-x_n

Solution:

What is the primary use of the Runge-Kutta method?

Solving non-linear equations

Solving linear simultaneous equations

Solving ordinary differential equations

Numerical integration

Solution:

When the Newton-Raphson method is applied to solve the equation f(x) = x³ + 2x - 1 = 0 with an initial guess value of x₀ = 1.2, the solution at the end of the 1st iteration is:

0.705

0.805

0.605

0.905

Solution:

The square root of a number a is to be obtained by applying the Newton-Raphson iteration to the equation x² - a = 0. The correct iteration scheme is:

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

x_n+1 = (x_n + a)/2

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

x_n+1 = (x_n - a/x_n)/2

Solution:

The Gauss-Seidel iterative method can be used for solving a set of:

Linear differential equations only

Linear algebraic equations only

Both linear and non-linear algebraic equations

Both linear and non-linear differential equations

Solution:

The equation x² - 4x + 4 = 0 is to be solved using the Newton-Raphson method to get a new estimate, and then the Secant method is applied using the initial guess and the new estimate. If the initial guess is 3, the estimated value of the root after the Secant method is:

10/3

7/5

7/3

5/3

Numerical-methods Questions Set 3:

If μ is the mean of the distribution, then Σf_i(x_i - μ) is

Solution:

What is the condition of failure for the Newton-Raphson method?

Solution:

Which of these is not a numerical integration method?

Solution:

If e⁰ = 1, e¹ = 2.72, e² = 7.39, e³ = 20.09, and e⁴ = 54.60, then the value of the integral ∫₀⁴ e^x dx using Simpson's 1/3 rule is:

Solution:

The approximate root after n+1 iterations of the function x = e^-x using the Newton-Raphson method is:

Solution:

What is the primary use of the Runge-Kutta method?

Solution:

When the Newton-Raphson method is applied to solve the equation f(x) = x³ + 2x - 1 = 0 with an initial guess value of x₀ = 1.2, the solution at the end of the 1st iteration is:

Solution:

The square root of a number a is to be obtained by applying the Newton-Raphson iteration to the equation x² - a = 0. The correct iteration scheme is:

Solution:

The Gauss-Seidel iterative method can be used for solving a set of:

Solution:

The equation x² - 4x + 4 = 0 is to be solved using the Newton-Raphson method to get a new estimate, and then the Secant method is applied using the initial guess and the new estimate. If the initial guess is 3, the estimated value of the root after the Secant method is:

Solution:

Related Question Sets:

Related Topics:

Numerical-methods Questions Set 3:

If μ is the mean of the distribution, then Σfi(xi - μ) is

Solution:

What is the condition of failure for the Newton-Raphson method?

Solution:

Which of these is not a numerical integration method?

Solution:

If e0 = 1, e1 = 2.72, e2 = 7.39, e3 = 20.09, and e4 = 54.60, then the value of the integral ∫04 ex dx using Simpson's 1/3 rule is:

Solution:

The approximate root after n+1 iterations of the function x = e-x using the Newton-Raphson method is:

Solution:

What is the primary use of the Runge-Kutta method?

Solution:

When the Newton-Raphson method is applied to solve the equation f(x) = x3 + 2x - 1 = 0 with an initial guess value of x0 = 1.2, the solution at the end of the 1st iteration is:

Solution:

The square root of a number a is to be obtained by applying the Newton-Raphson iteration to the equation x2 - a = 0. The correct iteration scheme is:

Solution:

The Gauss-Seidel iterative method can be used for solving a set of:

Solution:

The equation x2 - 4x + 4 = 0 is to be solved using the Newton-Raphson method to get a new estimate, and then the Secant method is applied using the initial guess and the new estimate. If the initial guess is 3, the estimated value of the root after the Secant method is:

Solution:

Related Question Sets:

Related Topics:

If μ is the mean of the distribution, then Σf_i(x_i - μ) is

If e⁰ = 1, e¹ = 2.72, e² = 7.39, e³ = 20.09, and e⁴ = 54.60, then the value of the integral ∫₀⁴ e^x dx using Simpson's 1/3 rule is:

The approximate root after n+1 iterations of the function x = e^-x using the Newton-Raphson method is:

When the Newton-Raphson method is applied to solve the equation f(x) = x³ + 2x - 1 = 0 with an initial guess value of x₀ = 1.2, the solution at the end of the 1st iteration is:

The square root of a number a is to be obtained by applying the Newton-Raphson iteration to the equation x² - a = 0. The correct iteration scheme is:

The equation x² - 4x + 4 = 0 is to be solved using the Newton-Raphson method to get a new estimate, and then the Secant method is applied using the initial guess and the new estimate. If the initial guess is 3, the estimated value of the root after the Secant method is: