The root of the function f(x) = x<sup>3</sup> + x - 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x<sub>0</sub> = 1 is

To solve the equation 2sin x = x, by Newton Raphson method, the initial guess value is chosen to be x = 2. Consider x in radius only. The value of x (in radius) obtained after one iteration will be closed to

A

-8.101

B

1.901

C

2.099

D

12.101

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

A

-0.82

B

0.49

C

0.705

D

1.69

The extremum (minimum or maximum) point of a function f(x) is to be determined by solving $$\frac{{{\text{df}}\left( {\text{x}} \right)}}{{{\text{dx}}}} = 0$$ using the Newton-Raphson method. Let f(x) = x³ - 6x and x₀ = 1 be the initial guess of x. The value of x after two iterations (x₂) is

A

0.0141

B

1.4142

C

1.4167

D

1.5000

The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x² - N = 0. If i denotes the iteration index, the correct iterative scheme will be

A

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

B

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{\text{x}}_{\text{i}}^2 + \frac{{\text{N}}}{{{\text{x}}_{\text{i}}^2}}} \right)$$

C

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{{{\text{N}}^2}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

D

$${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} - \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

Rithika had Rs 8000. She invested some of it in savings scheme P and the rest ofthe money in savings scheme Q. She invested for 3 years in savings scheme P and for2 years in savings scheme Q. savings scheme P offers SI at a rate of 20% pa whilesavings scheme Q compounded annually at the rate of 30% pa. The interest receivedfrom savings scheme P is 930 more than the interest received from savings scheme Q.If Rs 1500 is debited from the invested amount of savings scheme P then find thedifference between the amount invested by Rithika in savings scheme P & savingsscheme Q.

A

Rs 200

B

Rs 300

C

Rs 400

D

Rs 500

In the Newton-Raphson method, an initial guess of x₀ = 2 is made and the sequence x₀, x₁, x₂ ... is obtained for the function 0.75x³ - 2x² - 2x + 4 = 0
Consider the statements
I. x₃ = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Newton-Raphson method is used to compute a root of the equation x² - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is

A

3.575

B

3.677

C

3.667

D

3.607

Identify the Newton-Raphson iteration scheme for finding the square root of 2.

A

$${{\text{x}}_{{\text{n}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{n}}} + \frac{2}{{{{\text{x}}_{\text{n}}}}}} \right)$$

B

$${{\text{x}}_{{\text{n}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{n}}} - \frac{2}{{{{\text{x}}_{\text{n}}}}}} \right)$$

C

$${{\text{x}}_{{\text{n}} + 1}} = \frac{2}{{{{\text{x}}_{\text{n}}}}}$$

D

$${{\text{x}}_{{\text{n}} + 1}} = \sqrt {2 + {{\text{x}}_{\text{n}}}} $$

A person invested Rs.2500 more in scheme B than that in scheme A. Scheme A offers 24% simple rate of interest and scheme B offers 20% annual rate of compound interest. If Interest from scheme A after 4 years is Rs.1080 more than that from scheme B after 3 years, then what is the ratio of amount invested in scheme A to that in scheme B?

A

5 ∶ 6

B

4 ∶ 5

C

7 ∶ 8

D

2 ∶ 3

A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale).
Numerical Methods mcq question image

If we use the Newton-Raphson method to find the roots of f(x) = 0 using x₀, x₁ and x₂ respectively as initial guesses, the roots obtained would be

A

1.3, 0.6 and 0.6 respectively

B

0.6, 0.6 and 1.3 respectively

C

1.3, 1.3 and 0.6 respectively

D

1.3, 0.6 and 1.3 respectively

The root of the function f(x) = x³ + x - 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x₀ = 1 is

Related Questions

The root of the function f(x) = x3 + x - 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x0 = 1 is

Related Questions

The root of the function f(x) = x³ + x - 1 obtained after first iteration on application of Newton Raphson scheme using an initial guess of x₀ = 1 is