Math 120: Assignment 2 (Due Tue., Sep. 18 at start of class)
Suggested practice problems (from Adams, 6th ed.):
1.2: 1,3,5,11,13,15,21,25,29,33,57,59,61,63,65,67,75,77,79
1.3: 3,7,9,11,13,19,21, 25 - 55 (the odd ones)
1.4: 1, 5-17 (odd), 29, 31 1.5: 1,5,7,11,17, 21-33 (odd), 37
Ch. review: 5-27 (odd), 31, 35, 37, and challenging problems 3 - 11 (odd)
Problems to hand in:
1. Evaluate the limit or explain why it does not exist:
√
(a) limx→64 (x1/3 + 3 x)
(2+h)−2 − 41
√ h
limx→1− x2 + x
3 √
limx→1 x1−−√xx
(b) limh→0
(c)
(d)
−2
|x+4|
x+4
(2x2 −3x)2
limx→1.5 |2x−3|
limx→−∞ √3x2x−1
2 +x+1
(e) limx→−4
(f)
(g)
2. Let f (x) =
x2 if x is rational
. Prove that limx→0 f (x) = 0.
0 if x is irrational
3
−t|
. Find the one-sided limits of f at t = −1, 0, 1 (including limits
3. Let f (t) = |2tt3 −t
±∞ if appropriate), and find limt→±∞ f (t). What are the horizontal and vertical
asymptotes of the graph y = f (t)?
4. Find the points at which f is discontinuous. At which of these points is f right or left
continuous? Sketch the graph of f .

x < −1
 2x + 1
3x
−1 ≤ x ≤ 1
(a) f (x) =

2x − 1
x>1
 √
x<0
 −x
1
0≤x≤1
(b) f (x) =
 √
x
x>1
5. If g(x) = −x5 − x4 + x2 + 1, prove that there are at least 2 numbers c such that
g(c) = 1.
6. Using the definition of limit, prove:
(a) limx→−3 (5 + 3x) = −4
(b) limx→2 x3 = 8
(c) that if limx→a g(x) = M 6= 0, then limx→a
Sep. 17
1
1
g(x)
=
1
M
(i.e. do problem 35 of 1.5).