Question

3. 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) 10/3
b) 4/3
c) 7/3
d) 13/3​

Answer 1

Answer:

a) 10/3

Step-by-step explanation:

Explanation: Iterative formula for Newton Raphson method is given by

x(1)=x(0)+f(x(0))f′x(x(0)).

Hence x0=6 (initial guess), f(x0)=32 and f’(x0)=12.

Substituting the values in the equation we get x1= 10/3.

Answer 2

The value of x¹ is $\frac{10}{3}$

Given:

f(x) = x² - 4 = 0

To Find:

The value of x¹

Formula used:

Newton Raphson formula.

Explanation:

Iterative formula for Newton Raphson method = x(1) = x(0) + $\frac{f(x(0))}{f'x(0))}$         (a)

Thus, x₀ = 6 (initial guess)

f(x₀)  = 6² - 4 (substituting the value of x = 6 in the equation)

       = 32

f'(x₀) = 12

Substituting the value of x₀ ,f(x₀), f'(x₀) in the equation (a) we will get

x₁ = $6 + \frac{32}{12}$

x₁  as $\frac{10}{3}$ .