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

**zzhenif** · December 12th 2012, 06:24 AM

I am currently working on these 2 problem on the picture but I am not sure if I am doing it right. Any help will be very appreciated.... Thanks

**Drexel28** · December 12th 2012, 11:15 AM

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.

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