Consider the function g(x) = x/√ 1 + x2, which has a single root at x = 0. For what starting values of x will Newton’s method converge to 0? For what values will Newton’s method diverge? As in...

Consider the function g(x) = x/√ 1 + x2, which has a single root at x = 0. For what starting values of x will Newton’s method converge to 0? For what values will Newton’s method diverge?

As in Exercise 8.9, analyze the convergence of Newton’s method applied to the function f(y) = yp − x for p = 3, 4,... and also for p = −1 (for computers with no floating point division instruction).