(Group) Quiz 2: Sections 2.5 and 2.7
Please show your work and leave comments; your grade is based upon the steps you take completing a
problem, not solely on the final answer. You must write
YOUR NAMES!!
and then clearly answer the following questions:
sin(t)
.
arctan
e
(i) Evaluate the limit lim
5π
t→
2
(3 + h)−1 − 3−1
.
h→0
h
(ii) Evaluate the limit lim
√
√
a + 2h − a
(iii) Evaluate the limit in terms of the constant a: lim
.
h→0
h
2 − |x|
.
x→−2 2 + x
(iv) Evaluate the limit lim
(v) Find the horizontal asymptotes, if any exist, of the function f (x) =
√
9x2 + x − 3x.
x2 (vi) Find the horizontal asymptotes, if any exist, of the function g(x) = arctan e x−1 .