CME 100
Fall 2010
Vector Calculus for Engineers
Page 1 of 2
Prof. Eric Darve
Homework 1 – Due 9/24
Homework on prerequisites
This homework tests your knowledge of prerequisite material. It will also be used to form the teams.
You have to do this homework by yourself with no outside help. You may use any textbook or written
material to help you ﬁnd the answers. You cannot discuss this homework with other students. You may ask
clariﬁcations to the teaching assistants or the instructor, but they will not help you solve the problems. You
cannot use a calculator.
The di
ﬃ
culty of the problems varies from relatively straightforward to di
ﬃ
cult. You may not be able to
solve all these problems. That does not imply you will not do well in this class.
Exercises:
1. Find the limit:
lim
x
→
0
cos(
x
+
sin(
x
))
2. Find the limit:
lim
x
→
0
1

√
1

x
2
x
3. Di
ﬃ
cult problem. The ﬁgure shows an isoceles triangle
ABC
(

AB

=

AC

). We assume that the
height
h
=

AM

is varying and approaches 0. The bisector between
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 '08
 DARVE,KHAYMS
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