(60 points) This parts consists of 24 multiple choice problems. Nothing more than
the answer is required; consequently no partial credit will be awarded. Fill in your
answer for each problem in the box at the bottom of every page.
1. Find lim
x!0
sin x
.
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Section 1.1 HW
Please give complete, well written solutions to the following exercises.
1. A rectangle has an area of 16 cm2 . Express perimeter as a function of
length of one of its sides and find the domain of this function.
2. Sketch the region in the
Section 1.3 HW
Please give complete, well written solutions to the following exercises.
1. Exercise Problem 22 on page 34.
(Graphs are to be sketched on your HW by hand - based on what you
see on your calculator or graphing software like www.wolframalpha.
Solved Examples from Chapter 5
I understand that you will have a very short time to study chapter 5 and I could not cover as
many examples as I would have liked to in class. So this is a document in which I am giving you
written solutions to dierent kinds
Examples from Ch. 5: 5.3 and 5.4
Section 5.3: Evaluating Integrals
Problem 1: Evaluate the following Integrals:
In the following, you will need to use the Evaluation Theorem.
5 ex + 3 sin x dx = [5ex 3 cos x] = (5 e 3(1) (5 e0 3(1) = 5e + 1.
0
1)
0
1
5 x
Math 131
Midterm Examination 3 April 7, 2009
Name
General Instructions: You may use a simple calculator that is not graphing or programmable. You may have a 3x5 card, but no other notes.
Part I (70 points): For each of the following 17 problems, mark your
Math 155
Exam 3A
NAME:
Section #
October 21, 2003
SSN: X X X X X
Listen very carefully to the examiner as testing procedures are explained. Before working
on any problems, write your student ID# on the exam as well as at the top right portion
(marked by t
Practice problems from old Midterms
These problems are collected from several dierent midterms and represent a sample of the kinds
of questions in the midterms. This is by no means to be considered as exhaustive and for more
practice, you should look at s
Practice problems from old Midterms
Problems numbered exactly like in the Problem set:
5.
f (x) =
3
x, a = 1000,
3
1003 = 10 + f (1000)(1003 1000) = 10.01
5.
(a) exponentiate both sides and solve. f 1 (x) =
(b) And:
2 .
13
3
ex 1. Domain is all real numbe
Finals Practice Problems
=0
formulas: f' = (e^(-2t)/ -2 + 2 sin (t/2) + C
f = (e^(-2t)/ 4 - 4 cos (t/2) + C t + D
plugin conditions and nd C and D
C = 1/2
D = 15/4
1
Use Wolfram alpha to see the
graph.
0
innity
innity
innity
(2x -1) e^(1/x)
2
Note: 0 is n