Question

find by newton's method correct 4 decimals the root between 0 and 1 the equation 3x-cosx-1​

Answer 1

Step-by-step explanation:

Root : x= 0.607102

Step-by-step explanation:

In Newton- Raphson method, we use the formula to find the roots.

x_n = x_n - \frac{f(x_n)}{f'(x_n)}

f

′

(x

n

)

f(x

n

)

f(x) = 3x-cosx-1

f'(x)= 3+sinx

Lets start with x_1 = 0.5

x_2 = 0.5 - \frac{3(0.5)-Cos(0.5)-1}{3+sin(0.5)}

3+sin(0.5)

3(0.5)−Cos(0.5)−1

= 0.5 - (-0.108)

x_2 = 0.608

Next, x_3 = 0.608 - \frac{3(0.608)-Cos(0.608)-1}{3+sin(0.608)}

3+sin(0.608)

3(0.608)−Cos(0.608)−1

= 0.608 - 0.000898

x_3 = 0.607102

Hence, the real root is 0.607102. Continuing further. we get the values near to it..