Solution, the variable $${x_1}$$ and $${x_2}$$ for the following equations is to be obtained by employing the Newton $$-$$ Raphson iteration method
equation (i) $$10\,{x_2}\,\sin \,{x_1} - 0.8 = 0$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$10\,x_2^2\, - 10\,{x_2}\cos \,{x_1} - 0.6 = 0$$
Assuming the initial values $${x_1} = 0.0$$ and $${x_2} = 1.0$$ the Jacobian matrix is

Given $$f(t)$$ and $$g(t)$$ as shown below

$$g(t)$$ can be expressed as

Given $$f(t)$$ and $$g(t)$$ as shown below

The laplace transform of $$g(t)$$ is

A point $$z$$ has been plotted in the complex plane as shown in the figure below

The plot of the complex number $$w = 1/z$$