Consider the difference equation yn+2 = yn + yn−1 with starting values all equal to 1. What is the limit of the ratio yn+1/yn as n → ∞? Consider the function g(x) = x/√ 1 + x2, which has a single root...

Consider the difference equation yn+2 = yn + yn−1 with starting values all equal to 1. What is the limit of the ratio yn+1/yn as n → ∞?

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?