Question

Q.3 Find by al Newton Raphson method, the real root of the equation 3x=cosx+1.​

Answer 1

Step-by-step explanation:

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

x_n=x_n f(xn) f'(xn)

f(x) = 3x-cosx-1

f'(x)= 3+sinx

Lets start with x_1 = 0.5

X_2 = 0.5-3(0.5)-Cos(0.5)-1 3+sin(0.5)

= 0.5-(-0.108)

X_2 = 0.608

Next, x_3= 0.608-3(0.608)-Cos(0.608)-1

3+sin(0.608)

= 0.608 - 0.000898

x_3= 0.607102

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