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