University of Illinois
Fall 2009
ECE 313:
Problem Set 0
Calculus Review
Due:
Friday
August 28 at 4 p.m.
Reading:
Ross
Chapter 1.1–1.4, Chapter 2.1–2.5.
Noncredit Exercises:
Chap. 1: Probs. 15,7,9.
Theoretical exercises 4,8,13. Selftest probs. 115.
Chap. 2: Probs. 3,4,9,10, 1114.
Theoretical exerecises 13,6,7,10,11,12,16,19,20.
Selftest probs. 18.
About the problems below:
Calculus, a prerequisite of this course, will be used mainly in the second
half of the semester. The parts of calculus primarily needed are integration and diﬀerentiation, Taylor series,
L’Hˆ
opital’s Rule, integration by parts, and double integrals (setting up limits of integration and change of
variables such as in rectangular to polar coordinates). This problem set will help you review these topics,
and identify areas in which you may need additional review.
1.
[Geometric, MacLaurin, and Taylor series; L’Hˆopital’s rule]
(a) Prove that 1 +
x
+
x
2
+
···
+
x
n

1
=
1

x
n
1

x
for all
x
6
= 1 and all integers