Math 1210-001
Homework 1
Due May 28, 2013
This homework assignment is designed to go along with sections 1.1 through
1.5 of your textbook, which we have completed in class. The majority of
your score will be based on how you organize and demonstrate the process of
solving each problem. To that end, make sure your work is neat, legible,
well-organized and self-explanatory. You must staple your assignment to
receive full credit.
Name:
1. (10 points) Use Theorem A from section 1.3 (labeled “Theorem 1” in your class notes
for that section) to calculate the following limit. At each step, list which part of the
theorem you are using. For an example of how to illustrate your work, see Examples 1-4
in section 1.3.
3
1/3
4y + 8y
lim
y→2
y+4
2. (10 points) Given that
lim f (x) = 3 and lim g(x) = −1,
x→a
x→a
calculate the following limit or state that it does not exist:
lim [|f (t)| + |3g(t)|]
t→a
3. (10 points) Find the horizontal and vertical asymptotes for the graph of the function
3
F (x) =
. Show the specific limits that allow you to conclude that a particular
9 − x2
line is a horizontal or vertical asymptote.
4. (10 points) Calculate the following limit:
√
√
lim ( 2x2 + 3 − 2x2 − 5)
x→∞
√
√
Hint: Multiply and divide by ( 2x2 + 3 + 2x2 − 5).
5. (10 points) Calculate the following limit, or state that it does not exist:
sin(3θ) + 4θ
θ→0
θ sec(θ)
lim