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