1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step sizes h = 1 and h = 0:5 (and two different colors).
2. Newton’s Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose you have just poured a cup of coffee with temperature 95 C in a room where the temperature is 20 C. Using Newton’s law, write a differential equation for the temperature of the coffee as a function of time. What is the initial condition?