Let g e C'fa, fej and p be in (a, b) with g(p) = p and |g'(p)| > 1. Show thatthere exists a <5 > 0 such that if 0 < |po p\ < <5, then |po pi < Ipi p\ Thus, no matter how close the initial approximation po is to p, the next iterate p\ is farther away, so the fixed-point iteration does not converge if/?o i 1 P

MATH 23 WEEK 2 NOTES MODELING WITH DIFF EQ Solvent-solute mixture problems: goal is to compute the amount (Q(t)) of solvent in the tank at the time t. ) = − Assumptions: Volume of water (V(t)) is constant if rate in = rate out Concentration of solvent is constant Mixture is well stirred Concentration of inflow = c lb/gal Concentration of outflow is c(t) lb/gal ) = ) Units are impor