Greenwood press

ASYMPTOTE
7
Graph of 
f (x) =
x−2
x+3
with asymptotes at 
x = −3
and
y = 1.
A graph of the temperature, 
in degrees Fahrenheit, of coffee 
as a function of the number of
minutes it sits in a closed cup. 
The temperature of the coffee 
levels off near room temperature
after an hour and a half.

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asymptote. In both cases, the asymptote would represent the room temperature,
because the liquid either warms or cools to that temperature after it is left out for
awhile.
Scientific barriers based on speed are asymptotic until technological ad-
vances overcome a barrier. For example, airplanes could not pass the sound bar-
rier, called Mach 1, until 1947. (See Ratio.) Before that time, airplanes progres-
sively became faster and faster, approaching the speed of sound but unable to
surpass it, because they were not built to handle the shock waves produced at
such speeds. However, once the barrier was broken, scientists and engineers were
given data that helped them develop airplanes that could maintain their structural
integrity under the stressful conditions associated with travel at those speeds.
Today, particle physicists are challenging the speed of light by accelerating par-
ticles in large circular chambers. As testing and experimentation progresses over
time, the detected speeds of particles have been gradually approaching the bar-
rier of 
3 × 10
8
meters per second. Scientists argue whether it will be possible to
move at speeds faster than light, and if so, what type of consequence will occur.
Many science-fiction stories portray ships disappearing when they travel faster
than the speed of light, because light is not fast enough to show an image of the
ship to an observer.
Terminal velocity is the limiting speed of an object due to wind resistance
when it is in free-fall. For example, a skydiver will jump out of an airplane and
be pulled towards the earth at an acceleration of 9.8 meters per second squared.
This means that the velocity of the person falling will gradually increase until it
reaches terminal velocity. The equation 
v = 9.8t describes the velocity, v, in
meters per second of a person falling out of the plane after 
t seconds. After 1 sec-
ond, the skydiver is falling at a rate of 9.8 meters per second, and after 2 seconds,
the person’s velocity has increased to 19.6 meters per second. However, if the
skydiver lies flat during free-fall, the wind resistance will inhibit the falling rate
so that the body does not exceed 50 meters per second. Consequently, 
y = 50
becomes the horizontal asymptote on the velocity versus time graph. This infor-
mation is helpful for the skydiver to determine how much time can be spent in
the air for skydiving acrobatics and at what point the parachute should be opened
for safe landing.
Vertical asymptotes typically appear in applications that deal with improba-
ble events, costs, or quantities. For example, the cost to extract petroleum from
the Earth is dependent on its depth. Oil that is deeper underground will typically
be more expensive to remove, because it is more difficult to create deeper tun-