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Engineering Mathematics Question on Differential Equations

To solve the equation x = 2 cos x using Newton-Raphson's method, which one of the following iterations should be used ?

A

xn+1=xn−xn−2cos⁡xn1+2sin⁡xnx_{n+1}=x_n-\frac{x_n-2\cos x_n}{1+2\sin x_n}

B

xn+1=xn+xn−2cos⁡xn1+2sin⁡xnx_{n+1}=x_n+\frac{x_n-2\cos x_n}{1+2\sin x_n}

C

xn+1=xn+1+2sin⁡xnxn−2cos⁡xnx_{n+1}=x_n+\frac{1+2\sin x_n}{x_n-2\cos x_n}

D

xn+1=xn−1+2sin⁡xnxn−2cos⁡xnx_{n+1}=x_n-\frac{1+2\sin x_n}{x_n-2\cos x_n}

Answer

xn+1=xn−xn−2cos⁡xn1+2sin⁡xnx_{n+1}=x_n-\frac{x_n-2\cos x_n}{1+2\sin x_n}

Explanation

Solution

The correct option is (A) : xn+1=xn−xn−2cos⁡xn1+2sin⁡xnx_{n+1}=x_n-\frac{x_n-2\cos x_n}{1+2\sin x_n}.