Question

the equation f(x) is given x3-x2+4x=0. Consider the approximation of x=2 then the value if next approximation correct upto 2 decimal places is given as a)0.67 b)1.33 c)1.00 d)1.50​

Answer 1

Step-by-step explanation:

Given the equation f(x) is given x3-x2+4x=0. Consider the approximation of x=2 then the value if next approximation correct up to 2 decimal places is

• We need to find the value of the next approximation for the given equation.
• So we have
•     f(x) = x^3 – x^2 + 4x = 0
• So the approximation is x = 2
•        So f(x) = x^3 – x^2 + 4x = 0
•             f(2) = 2^3 – 2^2 + 4(2)
•                  = 8 – 4 + 8
•                  = 12
•     f’(x) = 3x^2 – 2x + 4
•     f’(2) = 3(2)^2 – 2(2) + 4
•           = 12 – 4 + 4  
•           = 12
• Now we have
•               x2 = 2
•       xn + 1 = xn – f(xn) / f’(xn)  
•          x3 =  2 – 12 / 12
•              = 2 – 1
•             = 1
• Therefore the value of next approximation is 1.00

Reference link will be

https://brainly.in/question/22279773