Math 2250 HW #2
Due 12:30 PM Thursday, August 22
Reading: Strogatz “Take It to the Limit” (http://opinionator.blogs.nytimes.com/2010/
04/04/take-it-to-the-limit/), Hass §2.2,2.4–2.5
Problems: Do the assignment “HW2” on WebWork. In addition, write up solutions to the
following problems and hand in your solutions in class on Thursday.
1. Evaluate the following limit or explain why it doesn’t exist:
√
x−3
lim
.
x→9 x − 9
2. Draw the graph of a function g(x) for which each of the following is true:
· lim g(x) = 4
x→−2
· g(−2) = 1
· lim g(x) = g(0) = 2
x→0
· lim g(x) = g(1) = 0
x→1−
· lim g(x) = 3
x→1+
3. Einstein’s theory of special relativity says that the apparent length of a spaceship depends on
how fast the spaceship is moving relative to an observer (this is known as “length dilation”).
Specifically, if the observer measures the spaceship’s length to be L0 when the spaceship is at
rest, then the length of the spaceship (as a function of velocity) is
r
v2
L(v) = L0 1 − 2 ,
c
where c is the speed of light. What happens to the apparent length of the spaceship as its
velocity approaches the speed of light from below? (Hint: write this as a one-sided limit,
then evaluate the limit.)
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