Math 2250 HW #12 Due 12:30 PM Thursday, October 31 Reading: Hass §4.5–4.6 Problems: Do the assignment “HW12” on WebWork. In addition, write up solutions to the following problems and hand in your solutions in class on Thursday. 1. A large international jet (like a Boeing 747 or an Airbus A340) typically has a takeoff speed at sea level of about 80 m/s (which is approximately 180 mph), and needs to get up to that speed within the 3000 meters of a typical international runway. Assuming the engines provide a constant acceleration and the plane starts from rest, what’s the minimum acceleration needed to ensure the plane will take off? 2. Evaluate the limit 1 x lim 1+ . x→+∞ x (Although you derived this as a consequence, some people treat this as the definition of this number.) 3. Use your knowledge of calculus to draw the graph of the function f (x) = x2 ex . In particular, be sure to label any inflection points, local maxima, and local minima, and if the function has an absolute minimum and/or an absolute maximum, find them. 1