Math 1210
Quiz 1
January 10th, 2014
Answer four (4) of the five (5) questions below. Please indicate which
questions you want to have graded. Every question is worth the same. You
may use scratch paper, but you can only turn in this sheet. No cell phones,
calculators, notes, or music players are allowed during the quiz.
Name:
Which 4 questions do you want to have graded?:
UID:
1. Suppose that f (x)g(x) = 1 for every x and that limx→a g(x) = 0. In the following
argument, which of the 4 steps is wrong and what is wrong with it?
1. Since f (x)g(x) = 1, taking limits on both sides we obtain
lim [f (x)g(x)] = lim 1 = 1
x→a
x→a
2. The limit of a product is the product of the limits so
h
i h
i
lim [f (x)g(x)] = lim f (x) · lim g(x)
x→a
x→a
x→a
3. Since limx→a g(x) = 0 we have
h
i h
i
lim f (x) · lim g(x) = 0
x→a
x→a
4. From all this we conclude that 0 = 1.
2. Find the limit
lim
x→1−
1
1
−
x − 1 |x − 1|
3. Find the limit
lim+
x→2
4. Find the limit
(x2 + 1)[[x]]
(3x − 1)2
2x2 − 6xπ + 4π 2
x→π
x2 − π 2
lim
5. Find the limits
lim [[x2 + 2x]],
x→3+
Page 2
lim [[x2 + 2x]]
x→3−