# I have 2 " Numerical analysis problems that I need help with

For the second one, merely check that the $k+1$st Newton iterate is $x_{k+1}=\frac{1}{2}\left(x_k+\frac{5}{x_k}\right)$. Now, I'm sure that you can prove that whatever your initial guess $x_0$ is, that this sequence will be monotone and bounded and so convergent.