Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p of g Show that if g '( p) 0 such that if p0 p , then the fixed point iteration converges Where g 32 17 ft s2 and k represents the coefficient of air resistance in lb s ft Suppose s0 300 ft, m 0 25 ...

Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p

Question:

Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p of g. Show that if |g'( p)| 0 such that if |p0 ˆ’ p| ‰¤ Î´, then the fixed-point iteration converges.

Where g = 32.17 ft/s2 and k represents the coefficient of air resistance in lb-s/ft. Suppose s0 = 300 ft, m = 0.25 lb, and k = 0.1 lb-s/ft. Find, to within 0.01 s, the time it takes this quarter-pounder to hit the ground.