22C:19 Discrete Math
Fall 2009
Hantao Zhang
So. What is it?
Discrete mathematics is the study of
mathematical structures that are fundamentally
discrete, in the sense of not supporting or
requiring the notion of continuity (wikipedia)
In other words, de
P1: 1
ANS
Rosen-2311T
MHIA017-Rosen-v5.cls
May 13, 2011
10:29
Answers to Odd-Numbered Exercises
CHAPTER 1
Section 1.1
1. a) Yes, T b) Yes, F c) Yes, T d) Yes, F e) No f) No
3. a) Mei does not have an MP3 player. b) There is pollution
in New Jersey. c) 2 +
Suggested Practice Problems
Math 229, Calculus I
Evaluate the following limits
x2 4x
x4 x2 3x 4
1. lim
(a) Try plugging in x = 4 to see what happens.
x2 4x
(4)2 4(4)
0
=
=
x4 x2 3x 4
(4)2 3(4) 4
0
lim
(b) This is called an indeterminate. It means we cant
Suggested Practice Problems
Math 229, Calculus I
Evaluate the following limits
1. lim
x1
3+x2
x1
(a) Try plugging in x = 1 to see what happens.
lim
x1
3+x2
=
x1
0
3+12
=
11
0
(b) This is called an indeterminate. It means we cant get the value by just plug
Honors Pre-Calculus
Limits Worksheet #5
Name_
May 2014
Use the graph to estimate the limits and function values, or explain why the limits do not exist or the function values
are undefined.
1.
2.
a.
a.
b.
b.
c.
c.
d.
( )
3.
d.
(
4.
a.
b.
b.
c.
c.
d.
d.
(
More Practice, Take Home Practice Test, Calculus Concepts: Limits and Derivatives
Name_
May 13, 2015
Open Ended. Show all work. Circle your final answer.
Decide whether the limit exists. If it exists, find its value.
1) lim f(x) and lim f(x)
x 0x 0+
2) li
PRECALCULUS
Name_
Limits Practice
Date_ Period_
Y J2D0g1d3T 0KwuttbaO 6SDoufJtCwrajrrer hLuLoCm.Q m 4AmlJlj Irai8gPhktZsK yrce4sgeErTv3eEd3.j
Evaluate each limit. Check your work using your graphing calculator.
1) lim ( x 2)
2) lim s
3) lim 2t
4) lim (s +
Math 19: Calculus
Summer 2010
Practice Problems on Limits and Continuity
1 A tank contains 10 liters of pure water. Salt water containing 20 grams of salt per liter
is pumped into the tank at 2 liters per minute.
1. Express the salt concentration C (t) af
Calculus 1
Chapter 2 Practice Test
Instructor: T. Hartman
Circle the letter of the correct choice. Work problems in the space provided.
1. Complete the table and use the result to estimate the limit.
x + 12
lim 2
x 12 x + 27 x + 180
x
f(x)
A)
B)
C)
D)
E)