If f(x) = x2-117 = 0 then the iterative formula for Newton Raphson Method is given by ____________ b) x(n+1)=0.5 c) x(n+1)=0.5 d) x(n+1)=0.25

If f(x) = x2 – 153 = 0 then the iterative formula for Newton Raphson Method is given by __________ b) x(n+1) = 0.5 c) x(n+1) = d) x(n+1) =

A

x(n+1) = 0.5

B

x(n)+$\frac{153}{x(n)}$

C

x(n)+$\frac{153}{x(n)}$

D

x(n)+$\frac{153}{x(n)}$

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

A

$${{\text{x}}_{{\text{k}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{k}}} + \frac{{117}}{{{{\text{x}}_{\text{k}}}}}} \right)$$

B

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - \frac{{117}}{{{{\text{x}}_{\text{k}}}}}$$

C

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - \frac{{{{\text{x}}_{\text{k}}}}}{{117}}$$

D

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - \frac{1}{2}\left( {{{\text{x}}_{\text{k}}} + \frac{{117}}{{{{\text{x}}_{\text{k}}}}}} \right)$$

The following equation needs to be numerically solved using the Newton-Raphson method. x³ + 4x - 9 = 0. The iterative equation for this purpose is (k indicates the iteration level)

A

$${{\text{x}}_{{\text{k}} + 1}} = \frac{{2{\text{x}}_{\text{k}}^3 + 9}}{{3{\text{x}}_{\text{k}}^2 + 4}}$$

B

$${{\text{x}}_{{\text{k}} + 1}} = \frac{{3{\text{x}}_{\text{k}}^2 + 4}}{{2{\text{x}}_{\text{k}}^2 + 9}}$$

C

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - 3{\text{x}}_{\text{k}}^2 + 4$$

D

$${{\text{x}}_{{\text{k}} + 1}} = \frac{{4{\text{x}}_{\text{k}}^2 + 3}}{{9{\text{x}}_{\text{k}}^2 + 2}}$$

Solution of the variables x₁ and x₂ for the following equations is to be obtained by employing the Newton-Raphson iterative method
equation (i) 10x₂ sin x₁ - 0.8 = 0
equation (ii) 10$${\text{x}}_2^2$$ - 10x₂ cos x₁ - 0.6 = 0
Assuming the initial values x₁ = 0.0 and x₂ = 1.0, the Jacobian matrix is

A

\\

B

\\

Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?

A

30

B

16

C

28

D

20

In Newton Raphson method f’(x) for a given point is given by the formula ____________

A

y/x’

B

y’/x

C

y/x

D

y’/x’

During a class experiment, a teacher took two objects and immersed them in water. She recorded the readings using a spring balance as shown below: Object Wt. of Stone in Air (Newton) Wt. of Stone in Water (Newton) Weight of Liquid Displaced (Newton) Buoyant Force acting on body (Newton) A 92 X 16 Y B Q 70 Z 10 Which of the following is correct?

A

X - 108, Y - 108, Z - 10, Q - 80

B

X - 108, Y - 16, Z - 80, Q - 80

C

X - 76, Y - 16, Z - 10, Q - 80

D

X - 76, Y - 16, Z - 80, Q - 10

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

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

The equation x³ - x² + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then the next approximation using this method will be

A

$$\frac{2}{3}$$

B

$$\frac{4}{3}$$

C

1

D

$$\frac{3}{2}$$

The Newton Raphson method is also called as ____________

A

Tangent method

B

Secant method

C

Chord method

D

Diameter method

If f(x) = x2-117 = 0 then the iterative formula for Newton Raphson Method is given by ____________ b) x(n+1)=0.5 c) x(n+1)=0.5 d) x(n+1)=0.25

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