The equation f(x) is given as x2-4=0. Considering the initial approximation at x = 6 then the value of x1 is given as ____________a)10/3b)4/3c)7/3d)13/3Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Solution:

To find the value of x1, we need to use the Newton-Raphson method, which is an iterative method for finding the roots of a function.

Step 1: Define the function

The given equation is f(x) = x^2 - 4.

Step 2: Find the derivative of the function

To use the Newton-Raphson method, we need to find the derivative of the function. In this case, the derivative of f(x) = x^2 - 4 is f'(x) = 2x.

Step 3: Perform the iteration

Using the initial approximation x = 6, we can perform the iteration to find the value of x1.

The Newton-Raphson iteration formula is given by:
x1 = x0 - f(x0)/f'(x0)

where x0 is the initial approximation.

Substituting the values into the formula, we have:
x1 = 6 - (6^2 - 4)/(2*6)
= 6 - (36 - 4)/12
= 6 - 32/12
= 6 - 8/3
= 18/3 - 8/3
= 10/3

Therefore, the value of x1 is 10/3.

Final Answer

The correct answer is option A) 10/3.

Answer

Iterative formula for Newton Raphson method is given by

Hence x0=6 (initial guess), f(x₀) = 32 and f’(x₀) = 12.
Substituting the values in the equation we get x₁ = 10/3.

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