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

Attachment 26192

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

For the second one, merely check that the st Newton iterate is . Now, I'm sure that you can prove that whatever your initial guess is, that this sequence will be monotone and bounded and so convergent.